Fractions Definition and 606 Threads

$\int\frac{6{x}^{2}+22x-23} {(2x-1)(x+3)(x-2)} dx $ Solve using partial fractions $\frac{A}{2x-1}+\frac{B}{x+3}-\frac{C}{x-2}$ I pursued got A=2 B=-1 C=-3 Then?

Hi PF Peeps! Something came up while I was studying for my QM1 class. Basically we want to represent operators as matrices and in one case the matrix element is defined by the formula : <m'|m> = \frac{h}{2\pi}\sqrt{\frac{15}{4} - m(m+1)} \delta_{m',m+1} But the thing is we know m takes on...

Homework Statement (4a/a+4)+(a+2/2a) Homework Equations Just combine and then factor out The Attempt at a Solution It's actually fairly simple, but I'm having difficulty at the end. /multiply each term by opposite denominator 4a(2a)/a+4(2a) + a+2(a+4)/2a(a+4) /combine 4a(2a)+(a+2)(a+4) /...

Okay so the name may be bigging it up however i found something in my maths class today that i don't think has previously been published or at least I've never been taught it, it makes converting reacuring decemals a lot quicker I know about the over 9 rule however acording to my maths teacher...

Homework Statement Evaluate Integrate (2-3x/(Sqrt.(1 - x^2))) dx Homework Equations 1/Sqrt.(1-x^2) = arctan The Attempt at a Solution I am so lost, but this is what I've tried, but didn't work... I separated the integral into two so Integral of (2/(Sqrt.(1-x^20))) dx - integral of...

Homework Statement Picture: http://matematikk.net/res/eksamen/1T/kort/1T_V11.pdf Task 5, the one the with a triangle inside a square. I'ts not in English so i'll transalate. I managed to do task a The picture above shows a square ABCD. The sides in the square have length 1. E is the center of...

When you divide a fraction, you minus the exponent - correct? Example: x^9/x^4 you take the 9-5 = 5 so it would be x^5 -correc?

Suppose we have a rational function ##P## defined by: $$P(x) = \frac{f(x)}{(x-a)(x-b)}$$ This is defined for all ##x##, except ##x = a## and ##x = b##. To decompose this function into partial fractions we do the following: $$\frac{f(x)}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b}$$ Multiplying...

Homework Statement ∫ [x^(3)+4] / [x^(2)+4] dx Homework Equations N/A The Attempt at a Solution I know that the fraction is improper, so I used long division to rewrite it as x+(-4x+4)/[x^(2)+4]. Given the form S(x)+R(x)/Q(x), Q(x) is a distinct irreducible quadratic factor [x^(2)+4]. I used...

Homework Statement I'm currently in Calculus 3, and the professor gave us a "retro assignment" which is basically a bunch of tough integrals from Calculus 2. I think my process here is valid, but when I check my answer on Wolfram, they're getting a slightly different final answer...

I was taught that when you have a polynomial fraction where the denominator is of a higher degree than the numerator, it can't be reduced any further. This seems wrong to me for a couple of reasons. 1. If the denominator can be factored some of the terms may cancel out 2. Say you have the...

Homework Statement integral(0>1) of (x^2+x)/(x^2+x+1)dx Homework Equations Factor denominator, and set numerator with A,B,C, etc. multiply both sides by the common denominator. The Attempt at a Solution Since the denominator won't factor at all I don't really know where to start, I could...

Hi all, I'm having a problem simplifying this: [1/(1+x+h) - 1/(1+x)] / h How do you get the common denominators for the top 2 fractions? Thanks

Kindly check this math. A. Homework Statement : Q1. There are 2100 pupils in a school. 1/3 of the pupils are girls. 2/5 of the girls can swim. How many girls can swim? Q2. 5 Whole 2 hundredths=? Q3. 3 Whole 8 tenths= ?B. The attempt at a solution Ans1: 2100 x 1/3= 700 700 x 2/5 =280 280...

Why, when a fraction has repeated linear terms in its denominator e.g. (11x2+14x+5)/[(x+1)2(2x+1)] does it have to be split into three partial fractions, A/(x+1) + B/(x+1)2 + C/(2x+1)? When my first saw this example, my initial reaction was to split it into A/(x+1)2 +B/(2x+1), but after working...

Homework Statement take inverse laplace of: 6/[s^4(s-2)^2] Homework Equations 6/[s^4(s-2)^2] The Attempt at a Solution I used partial fractions. I was wondering if It could be manipulated to where I could use the laplace table?

I'm a little empty on what to talk about. Only things that come to mind is normality (and mentioning Pi in that respect) and that 1/number's decimal expansion is only finite if its prime factors are 2 or 5. What else is there to talk about?

1. x^2-x+1 Is this factorable? My initial thinking is NO. However, I can complete the square and it becomes (x-1/2)^2-3/4, but this doesn't seem to help me. Would this be considered factorable? 2. Turn 1/x^2-x+1 into partial fractions Clearly, after I answer #1 correctly, #2 will be more...

I went to splash at MIT a while back, and I took a class on cesaro summation. We were promised to go over an interesting identity but we never did: ##4(\frac{1}{2}!)^2=\pi##. Now, this doesn't make any sense to me, since I thought you could only do factorials with integers, like in the famous...

Given: $$\frac{x-2}{x-5}>\frac{x-3}{x-4}$$ How I would normally solve it is to bring everything over to one side and find a common denominator. The answer of which is $x>5$ Now a commentary on this question says to "watch out" for sign changes if you multiply both sides by an expression, so I...

This is frustrating me. The formula for division of fractions in my Pre-Calculus book is a/b = a x 1/b. However, when you apply this to an actual problem, it doesn't make sense. For example: 3/4 divided by (sorry, I don't see a divisor sign in the list of symbols we can choose from) 6/11...

Someone eats \frac{4}{12} of a box of donuts. His friend eats \frac{2}{6} more than the first guy. How many more donuts did the second guy eat than the first one? This problem may seem easy, but I feel like it's so hard!

This is kind of a "dumb" question, but why do we multiply the numerators and denominators when multiplying fractions? For example: 1/5 x 2/3 = 2/15 Intuitively, I know why we need a common denominator when adding and subtracting fractions. We need to add apples to apples and oranges to...

Why can ratios be written as fractions? if there are 5 men in 20 people the ratio of men to total people is 5:20 which is 1:4. But when we write 1/4 it gives 0.25. And 0.25 means the magnitude of each part when 1 is divided into 4 equal parts. So how does ratio and fraction give a...

Iam reading Julian Havil's book, The Irrationals: A Story of the Numbers You Can't Count On. In Chapter 3 Havil is writing about progress in the eighteenth century in determining the nature of \pi and e through the use of continued fractions. He writes (pages 92 - 93): Can someone please...

Homework Statement Find the partial fractions for this expression. (((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1))) The Attempt at a Solution The final answer is 1/sqrt(n) - 1/(sqrt(n+1)) My work: A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n)) I am subbing in n = -1 and n = 0 to solve for...

I'm a little rusty with partial fractions, and I can't seem to find my error once I get up to that point. Homework Statement dy/dx = (y^2 - 1) / x Homework Equations The Attempt at a Solution Cross-mutliply x dy = (y^2 - 1) dx Divide by the appropriate terms dy / (y^2...

Hey guys, Here is another pair of questions that I'm doubting at the moment: I used partial fractions for A and got (Bx+C)/x^2 + Ax/(x-1)^2 + Dx(x-1) which led me to compute A=1, B=0, C= -1, and D=0, which already sounds off. Do you guys have any suggestions? Also, for 5b, I calculated B=...

Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.) \int \frac {5x^2 - 20x +45}{(2x+1)(x-2)^2}\, dx Homework Equations 5x^2 - 20x +45 = 5 (x^2 -4x +9) The Attempt at a Solution I'm able to come up with an...

First the example problem. This is an integral of the whole thing (3x^3+24x^2+56x-5) / (x^2+8x+17)^2 The answer comes out to be 3/2 ln(x^2+8x+17) - (49/2 tan^-1(x+4)) - (25x+105 / 2(x^2+8x+17) + C I would show all the steps but I'm still not sure on how to use the format tools, so that...

Hey guys, I'd really appreciate it if I could get some quick help for this problem set I'm working on. For question one, I just did a quick u substitution for x^4 and managed to get x^4 * sin(x^4)+cos(x^4) + C. For part b, I used integration by parts and took ln(4t) as u and the rest as...

What are some simplified conditions for which: $$W\bigg(A-\frac{X}{W}\bigg)^3\bigg[X-AW-\frac{AY}{N}(B+D)-\frac{AZ}{N}(C+D+E+F+G)\bigg]+\frac{X}{N}\bigg[Y(A+H)(B+D)+AZ(C+D+E+F+G)\bigg]<0$$ **WHERE:** All of the letters are positive parameters (not constants) and: $1.$ $$A,B,C,D,E,F,G,H < N...

Homework Statement For the equation shown below: x2+2x+3 / (x2+9)(X-3) = Ax+B/(x2+9) + C/(x-3) Find A, B and C Homework Equations The Attempt at a Solution C = 1 B = 2 A = ? Find C which = 1 by putting x=3 and working out x2+2x+3/(x2+9), then multiply out equation...

Hello, i've come across a partial fractions problem that I don't know how to solve - Usually, the denominator of the fraction I need to split up into two separate fractions is a quadratic, but in this instance it's a cubic. Specifically, the problem I'm having is that two of the factors to...

Sorry if this has been covered elsewhere but I'm having problems with equations such as this which are quadratics with fractions: 2 over 3x + 1 PLUS 3 over 1-x = 1/2. I know you are supposed to multiply each term by the product of the denominators but i keep getting weird results -so if...

Hello! I found the following problem on AOPS: Which is larger, $$\Large \frac{\int_{0}^{\frac{\pi}{2}}x^{2014}\sin^{2014}x\ dx}{\int_{0}^{\frac{\pi}{2}}x^{2013}\sin^{2013}x\ dx}\ \text{or}\ \frac{\int_{0}^{\frac{\pi}{2}}x^{2011}\sin^{2011}x\ dx}{\int_{0}^{\frac{\pi}{2}}x^{2012}\sin^{2012}x\...

Homework Statement Find the indefinite integral of the below, using partial fractions. \frac{4x^2+6x-1}{(x+3)(2x^2-1)} Homework Equations ?The Attempt at a Solution First I want to say there is probably a much easier and quicker way to get around certain things I have done but I have just...

When would you use trig substitution vs. partial fractions? I know partial fractions is when you have a polynomial over a polynomial, but some of the problems in the trig substitution section in my book had polynomial over polynomial and used trig substitution?

Homework Statement Find the partial fractions expansion in the following form, G(s) = \frac{1}{(s+1)(s^{2}+4)} = \frac{A}{s+1} + \frac{B}{s+j2} + \frac{B^{*}}{s-j2} Homework Equations The Attempt at a Solution I expanded things out and found the following, 1 = A(s^{2} + 4)...

Homework Statement Homework Equations After looking through this on Wiki, I'm a little confused as to how these partial fractions are multiplied out. Is there a rule or something for this? With simpler partials I can do it but this one is something else! The Attempt at a Solution

Homework Statement f = \frac{1}{z(z-1)(z-2)} Homework Equations Partial fraction The Attempt at a Solution R1 = 0 < z < 1 R2 = 1 < z < 2 R3 = z > 2 f = \frac{1}{z(z-1)(z-2)} = \frac{1}{z} * (\frac{A}{z-1} + \frac{B}{z-2}) Where A = -1 , B = 1. f = \frac{1}{z} *...

Hi, Sorry for the semi-book here I am working on a project where I am mixing h-BN nanoparticles into a polymer resin to try to tailor the thermal conductivity and dielectric strength of the resulting composite. Admittedly I am not very well versed when it comes to materials science...

\int (x+1/x2-3x-5)dx I can't put the limits on the integral sign, 5 is the top limit and 3 is the bottom limit. I can solve using partial fractions ok but I have never solved with limits before. Where do the limits come in, do I need them at the start or can I factorise as usual and use...

I have a separate question on the same problem from my prior post. I need an equation for a tangent which has a slope of 5/6 and passes through (1,3) y-3 = 5/6(x-1) I simplify this to y= 5/6x +13/6 However the answer given is y = 7/6(x) + 13/6 Where am I going wrong? Yours, Timothy

I have this derivative and I need the slope at (1,3). y' = [3(y-x)^2 -2x]/[3(y-x)^2] With this equation I plug in x and y and the slope equals 5/6. However, can't y' be simplified further to: y' = [3(y-x)^2]/[3(y-x)^2] -2x/[3(y-x)^2] ? Thus can't it be simplified to: y'= -2x/[3(y-x)]^2...

Homework Statement I have been working on this proof for a few hours and I can not make it work out. $$\sum_{i=1}^{n}\frac{1}{i(i+1)}=1-\frac{1}{(n+1)}$$ i need to get to $$1-\frac{1}{k+2}$$ I get as far as $$1-\frac{1}{k+1}+\frac{1}{(k+1)(k+2)}$$ then I have tried...

Homework Statement I have been working on this proof for a few hours and I can not make it work out. $$\sum_{i=1}^{n}\frac{1}{i(i+1)}=1-\frac{1}{(n+1)}$$ i need to get to $$1-\frac{1}{k+2}$$ I get as far as $$1-\frac{1}{k+1}+\frac{1}{(k+1)(k+2)}$$ then I have tried...

Homework Statement 1/ (x+8)(x^2+16) Find the integral Homework Equations I keep getting this question wrong. Can someone check my steps? The Attempt at a Solution I set it up as A/(x+8) + (Bx+C)/(x^2+16) So I did, A(x^2+16)+ (Bx+C)(x+8) and I did that and got A+b=0...

Homework Statement (2x^3-2x+1)/(x^2/3x) Find the integral. 2. The attempt at a solution So I've been on this problem for like an hour now and I don't know what I'm doing wrong. So I used long division and got 2x+ (4x+1)/(x^2-3x) ∫2x + ∫(4x+1)/(x^2-3x) = x^2 +...

We all know that 12/25 + 18/30 is not 30/55 yet students are happily told that they got 12 out of 25 in their first maths test and 18 out of 30 in their second maths test giving a total of 30 out of 55 So in this case 12/25 and 18/30 is 30/55 So should we be surprised when students say...