Fractions Definition and 607 Threads

Homework Statement Hi. My first post! I'm trying to solve for where a is a constant: ∫ (x/a)1/2*(x/(x-a)) dx Homework Equations See above The Attempt at a Solution I've tried integration by parts by setting u=(x/a)1/2 but I end up having to solve ∫ (x/a)1/2ln(x-a) - which I...

Homework Statement Show that if the simple continued fraction expression of the rational number \alpha , \alpha > 1 , is [a_0; a_1, a_2, \dotsc, a_k] , then the simple continued fraction expression of \frac{1}{\alpha} is [0; a_1, a_2, \dotsc, a_k] . Homework Equations The...

Homework Statement Ti-6Al-4V is a metal alloy used to make biomaterials. Its composition is 90% Ti; 6% Al and 4% V (mass percentages). (a) What are the mass fractions of Ti, Al and V? (b) What are the mole fractions of Ti, Al and V? Homework Equations Mass fraction = m/mtotal...

Homework Statement In one of the workings of a question I couldn't solve(from solution sheet) there was one step I couldn't understand. Homework Equations \frac{1}{x^2+x+1} = \frac{1-x}{1-x^3} The Attempt at a Solution Tried partial fractions(unfactorable denominator) and could'nt get it...

fractions -- showing that they are equivalent I have the fraction: a = c/d * b And from that I want to show that: a = c/(c+d) * (a+b) At least the two equations should be equivalent if I did everything right. How do I go from first to the second?

Homework Statement ∫(x3+4)/(x2+4)dx Homework Equations n/a The Attempt at a Solution I know I have to do long division before I can break this one up into partial fractions. So I x3+4 by x2+4 and got x with a remainder of -4x+4 to be written as x+(4-4x/x2+4). Then I rewrote...

Homework Statement We were given a worksheet to integrate some problems using partial fractions. This one however I cannot figure out what to do with it. This is the problem. ∫(x3-4x2+x+6)/(x2-x+2) dx The Attempt at a Solution using long division i got ∫(x-3) (-4(x-3)/(x2-x+2) dx...

$$ \frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z} $$I can't figure out how to decompose this fraction.

Homework Statement If I had a recurrence expression that recurs on partitions of size n - 1 each time, (as opposed some fraction of the original size ie. n/2), how can I apply the Master Theorem? I don't know what the "b" value is? Homework Equations The Attempt at a Solution...

Homework Statement If f is a quadratic function such that f(0) = 1 and \int \frac{f(x)}{x^2(x+1)^3}dx is a rational function, find the value of f '(0). Homework Equations The Attempt at a Solution This question is presented in the context of learning about integration by...

I'm taking a step back as I've found a concept I'm struggling with. If I have an equation: 2(x-1)/3 = (x/4)+1 I've been told I need to multiply by 12 to give me: 8(x-1) = 3x+12 However I'm struggling with the multiplication of fractions in his instance. Can anyone advise me how that...

Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate.) ∫(x^3 + 36)/(x^2 + 36) Homework Equations The Attempt at a Solution A little bit confused about arriving at the solution for this problem. I get stuck a little ways in. Any help would be...

i know you have the 3 row operations. add two rows. multiply a row by a constant. add a multiple of a row to another. my question is can you multiply a row by a constant to clear a fraction at any time so long as you end up in row echelon form. no matter what operations you do the result in...

y' = (3+y)(1-y) y(0) = 2 Attempt to solve: \frac{dy}{dx}=(3+y)(1-y) (3+y)(1-y)dy = dx \int(3+y)(1-y)dy = \int dx Partial Fractions: \frac{A}{(3+y)} + \frac{B}{(1-y)} A(1-y)+B(3+y) Let y= 1 or -3 A = 1/4 B = 1/4 \frac{1}{4}\int \frac{1}{(3+y)} dy + \frac{1}{4}\int...

Homework Statement \frac{x}{(x+4)^{2}} Homework Equations The Attempt at a Solution I make the integrand equal to the following: \frac{A}{(x+4)}+\frac{Bx+C}{(x+4)^{2}} Then after finding a common denominator I get x = A(x+4)^{2}+(Bx+C)(x+4) But that cannot be...

Homework Statement So I am trying to integrate the following. I believe I have to use partial fractions. \frac{1}{(x+4)^{2}(x-3)} Homework Equations The Attempt at a Solution So I am trying to expand the above into something that I can integrate. So I equated the integrand...

I just want to know if there is now a way to solve fractions like which had a variables that has a degree more than 2 in its denominator. I know that denominators having degrees of 2 could be solved using (Ax + B)/(x2+a). But how about denominators like (x3+a) and so on?

I have been trying to figure out how to plot a differential equation using my TI Nspire with very little luck. I managed to find that I can set the graph of the calculator to a directional field but I am not 100% sure I am getting the right results. So I figured I would ask to see if anyone here...

Hello all, Say one wants to find the inverse Laplace Transform of a function, and the method for attaining the solution is executed via partial fractions. Do the real numbers go with the complex numbers when determining the constants of partials? Perhaps this is wordy. I'll provide a theoretical...

step 1. [(3 - (3 + h))/(3(3+h))]/h step 2. -h/(3(3+h)h My book says that those steps are valid. I don't see how. If you want my opinion, I times the numerator (3 - (3 + h))/(3(3+h)) by the inverse of the denominator h/1 which makes: step 2. -h/(9+3h) * h step 3. -h/(9+3)...

How do I take (2/3) x (3 x 10^8)?

I did the first section of the question. I rearranged a = 4b / (6c -5d) to be c = (A b/a) + Bd but then it says express A and B as fractions in their simplest form. Is the question worded wrong? I've never seen anything like this before?

Homework Statement We know that for dry air, we have: -78.08% mol N2 ; -20.94% mol O2. This is: - Y(N2) = 0.7808 for nitrogen (the molar fraction in vapor) - Y (O2) = 0.2094 for oxygen Knowing that the Henry's law constants are: for N2 and O2 are 6.51 x 10^7 Torr and 3.3 x 10^7 Torr...

Homework Statement Use partial fractions to rewrite: (2z)/(z^2+3) Homework Equations noneThe Attempt at a Solution I did this: (2z)/(z^2+3) = (Az+B)/(z^2+3) 2z = Az +B A = 2, B = 0...problem is that it just recreates the original Here is their example in the book: 1/(z^2+1) =...

Homework Statement Find partial fractions for 4/(x^3-2x^2) The Attempt at a Solution Heres the steps that I took: 1. 4/(x^3-2x^2)= 4/(x^2(x-2))= A/(x^2) + B/(x-2) 2. 4= A(x-2) + B(x^2) 3. When x=0, -2A=4, so A=-2, and When x=2, 4B=4, so B=1. 4. So my final answer was: -2/(x^2)+1/(x-2) The...

Hey everyone, I was wondering if someone could help me understand what exactly is happening with a certain integral I am working with, which is as follows: ∫2/(u^2-1)du My steps are as follows (I used partial fractions): ∫(1/(u-1) - 1/(u+1))du = ∫1/(u-1)du - ∫1/(u+1) = ln[(u-1)/(u+1)]...

Homework Statement the definite integral of (x-1)/(x^3+4x^2+3x) from x=1 to x=3 using partial fraction decomposition. I know the answer should be (5/3)ln2 - ln3. Homework Equations The Attempt at a Solution After integrating, I got -(1/3)ln(3x) - (2/3)ln(x+3) + ln(x+1) . The...

Hi, I have a question regarding partial fractions. One of my Math lecturers said that to find partial fraction, we are actually finding the singularity points. I don't understand what happens at a singularity point that allows us to decompose a function into the sum of two other functions...

Homework Statement Expand Using Partial Fractions: f(x) = ( 5x-10 )/ ( (x+1)(x-4) ) Involves Integrating afterwards but I don't think this affects my method.Homework Equations This was a question in my mid semester exam, I got the answer correct but he insists my method is wrong.The Attempt at...

Homework Statement Integrate (x^3 - 8x^2 - 1)/((x+3)(x^2-4x+5)) Homework Equations This is an integration by partial fractions. The Attempt at a Solution http://www.wolframalpha.com/input/?i=integral+%28%28x^3-8x^2-1%29%2F%28%28x%2B3%29%28x^2-4x%2B5%29%29%29dx I understand everything...

\frac{-2x^2-x-3}{x^3+2x^2-x-2}=\frac{-2x^2-x-3}{(x-1)(x+1)(x+2)}=\frac{A}{x-1}+\frac{B}{x+1}+\frac{C}{x+2} Multiply by common denominator gives: -2x^2-x-3=A(x+1)(x+2)+B(x-1)(x+2)+C(x-1)(x+1)\Leftrightarrow -2x^2-x-3=Ax^2+A3x+A2+Bx^2+Bx-B2+Cx^2-C1 System of equations gives -2=A+B+C -1=A+B...

Homework Statement Find the partial fractions of 1/((3x)(5-x)) Homework Equations The Attempt at a Solution 1/((3x)(5-x))=A/(3x)+B/(5-x)=(A(5-x)+B(3x))/((3x)(5-x)) 1=A(5-x)+B(3x) If x=0 1=A(5-0)+B(3*0)=5A => A=1/5 If x=5 1=A(5-5)+B(3*5)=B15 => B=1/15 So...

Homework Statement May seem easy to people but I have no idea how to do this :frown: lim_{x\rightarrow0}\frac{sin x}{2x^{2}-x} Homework Equations The Attempt at a Solution I factored out an x from the bottom but that really makes me see nothing else to do.. So I tried the quotient...

\int\frac{7x^2+4x+5}{x^3+x} dx I have to solve this using partial fractions and all I could think of was breaking it up into: \frac{A}{x}+\frac{B}{x^2+1} also I tried \frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x} The reasoning behind this one was to split up original...

Homework Statement See attachment top left line Homework Equations See attachment took left line The Attempt at a Solution Follow left hand side of attachment. Thanks A

Homework Statement \int\frac{4x^5-1}{(x^5+x+1)^2}dx Homework Equations This is in the section on Partial Fractions. The main idea in this section was that you get the integral down to a sum integrals of the following forms: \int\frac{dx}{(x+a)^n} , \int \frac{x dx}{(x^2 + bx + c)^m} ...

the question asks me to balance the following equation C2H3NO + H2O ---> C2H8N2O + 2CO2 i attempted to balance it 2C2H3NO + H2O ---> C2H8N2O + 2CO2 i can't get all the oxygens to be equal, if someone can show me how to do this last step, id appreciate it also can one use...

what does this simplify to: (-33/2)2/3 I use the exponent rules to multiply the fractions to get (-31) which comes out to -3, but the answer key says the real answer is 3. Is there something important when doing fractional exponent that I'm missing out? Thanks in advance.

Homework Statement Ive been given a question that requires an answer in polar form but the method I must use is the normal addition/subtraction of fractions. This throws me because I'm sure there is a simple method for the reciprocal of a complex number. Q. 1/(13- 5i) - 1/(2-3i)...

Homework Statement Evaluate integral dx/(x^4-10x^2+9) Homework Equations The Attempt at a Solution Ok so I'm trying to solve this problem for my calculus II course as a homework problem and am lost. The first attachment you'll see how I attempted to evaluate the integral by...

Homework Statement seperate and solve using partial fractions dx/dt=9-4x2, x(0)=0 The Attempt at a Solution rearranging gives dx/(9-4x2) = dt factorising denominator in preperation for partial fractions becomes dx/(3-2x)(3+2x) then A/(3-2x) + B/(3+2x) dx so A(3+2x)+ B(3-2x)...

Homework Statement Someone teach me how to write equations using the editor here... This is part of an integration question need partial fractions of 1/(x^2)(x-4) Homework Equations -nil- The Attempt at a Solution 1/(x^2)(x-4)=(Ax+B)/(x^2)+C(x-4) Put x=0 therefore B=-1/4...

I've recently started development on a continued fraction based exact arithmetic computational package. This is work based on Bill Gosper's HACMEM algorithm and Peter Potts' Mobius transforms with significant modifications. These algorithms have some remarkable properties and can be made much...

Homework Statement Why is petrol suitable to be used as a fuel whereas lubricating oil is more suited to lubricate machine joints? Homework Equations The Attempt at a Solution Petrol has a low boiling point. It combusts more easily to provide energy to the car. However...

Integrate using partial fractions (arctan x) / ((x+1)(x^2+1))? My attempt: (arctan x) / ((x+1)(x^2+1)) = A/(x+1) + (Bx+C)/(x^2+1) arctan x = A(x^2+1) + (Bx+C)(x+1) when x= -1, A= -pi/8 so plugging in -pi/8 for B makes: x= tan[ (B-(pi/8))x^2 + (B+C)x + (C-(pi/8)) ] and when x=0, C=...

In this field, computer algorithms may produce false continued fraction expansions because of the limited accuracy in the floating point arithmetic used. Who knows more?

Hi, this is my first post, and I'm not sure if I'm posting this in the right place. Homework Statement I have a 2nd order diff. equation: 3y''(t) + 2y'(t) + 5y(t) = 3 with initial values: y'(0) = 1, y(0) = 0 Homework Equations After using Laplace transform I get: Y(s) = (3 +...

Hi all, Could anyone guide me on the following prove √2 = 1+1/(2 + 1/(2+ 1/(2+ 1/(2+···))))

I have a few questions about decomposing partial fractions. I know how to solve these problems, but I just don't understand why I'm doing some of the things. 1. Why does equating coefficients work? I don't understand the idea behind it. 2. When you are decomposing fractions into constants...

Homework Statement Simplify: 3c-(\frac{2a+c}{8}-\frac{a+2c}{4}) The Attempt at a Solution I got this: \frac{9c}{8} But the answer is: \frac{27c}{8} It's simply an issue with whether I find the LCM or I use this formula: \frac{a}{b}-\frac{e}{f}=\frac{a*f-b*e}{f*b} If...