Simplify Definition and 373 Threads

Mathematica -- how to simplify an output formula Hi all, Is there any more options to simplify an out put Mathematica formula. I used //Simplify but the expression still complicated and //FullSimplify too slow and didn't work. Bests, Safinaz

Homework Statement Simplify (x-2 - y-2) / (x-1 + y-1) Homework Equations The Attempt at a Solution So I just factorised the numerator into x-1 - y-1 and x-1 + y-1. And was left with x-1 - y-1 as an answer. The textbook gives (y - x) / (xy) as the answer (no working shown). So...

Homework Statement - 1/[cosx(cos(x-90))] The Attempt at a Solution = - 1/[cosx(-cos(90-x))] //so first I take the negative sign out from (x-90) to make it (90-x) = +1/[cosx(cos(90-x))] // negative sign from outside the cos and outside the entire fraction combine to...

Homework Statement Simplify the function and find the derivative; (Attached) Homework Equations I've had a go at the question (see below) trying to use trigonometric identities. The Attempt at a Solution I somehow arrived at 1/7 - 3/2sec^2, but I'm not sure that this is correct!

Hello, First time poster here. After lurking about the forums for a couple days I feel as if this question may be overly rudimentary; regardless, I'm stuck. This is not a homework assignment but preparation for an upcoming precalculus class. (x^2-4)((x^2+3)^1/2) - ((x^2-4)^2)...

I have this equation 1/(r^2+l^2)^(3/2) and I need to integrate it quickly. My first thought is using this integral formula 1/(1+x^2)^(3/2)=x/sqrt(1+x^2) but how exactly do I get my equation into that form?

Hello MHB, I am currently working with a old exam and it says.\lim_{x->0}\frac{3-e^{x^2}-2\cos(x)}{x^2\sin^2(x)} and this is how far I got but struggle on the simplify Regards, |\pi\rangle

$ a_n=(\dfrac{1}{\sqrt n+\sqrt {n-1}})\times(\dfrac{1}{\sqrt {n+1}+\sqrt {n-1}})\times(\dfrac{1}{\sqrt {n+1}+\sqrt n}) $ $S_n=a_1+a_2+a_3+-------+a_n$ $find:\,\, S_{2012}$

$\dfrac{3}{3\times 4}+\dfrac{4}{3\times 4\times 5}+\dfrac{5}{3\times 4\times 5\times 6}+\cdots+\dfrac {99}{3\times 4\times 5\times 6\times \cdots\times 99\times 100}$

Hello MHB, Simplify as far as possible without any calculator \frac{196707}{250971} Hint: Regards,

1. Simplify the derivative 2. y = \frac{\sqrt{1-x^{2}}}{x} 3. f'(x) = \frac{x*\frac{-2x}{2\sqrt{1-x^{2}}}-\sqrt{1-x^{2}}}{x^{2}}=\frac{-x^{2}-\sqrt{1-x^{2}}}{x^{2}\sqrt{1-x^{2}}} I just don't know how to simplify this further.

Simplify \sqrt{1+a^2+\sqrt{1+a^2+a^4}}.

Homework Statement Simplify the following trigonometric expression: cscθtanθsecθ Homework Equations tanθ = sinθ/cosθ sin^2θ + cos^2θ = 1 cscθ = 1/sinθ secθ = 1/cosθ cotθ = 1/tanθ The Attempt at a Solution I just want to double check my solution. cscθtanθsecθ = 1/sinθ x...

1. I am on the very last step of this problem, but I don't see how this equation simplifies from 2ln|(2/√(2)) + 1| - 2ln|1 + 0| to 2ln|√(2) + 1|.2. I thought that since ln|1| = 0, then 2x0=0. And then the answer would be: 2ln|2/√(2) +1|. I don't see how the 2 in the (2/√(2)) was canceled out...

Electric Dipole as x >> l, how do I simplify this correctly? Homework Statement ELECTRIC DIPOLE : 15.0 POINTS A charge −Q is located at x=−l/2 and a charge +Q is located at x=l/2. Thus the separation between the two charges is l. The total electric field on the x-axis can be written...

I'm working problem from the upper division classical mechanics course on MIT OCW. No solutions are available. This is form the first P-set, question 4. Homework Statement A particle moves in a two dimensional orbit defined by x = A(2αt-sin(αt)) y = A(1-cos(αt)) Find the tangential...

How do you know if you can can or can not simplify a boolean algebra expression further?

Why do I keep getting output that looks like this when I use Mathematica? $$\frac{2 b k |a+b v| (2 a+b v+b v \cos (t)) \sin ^2\left(\frac{t}{2}\right)}{(a+b v)^2 \sqrt{\left(\frac{1}{\sqrt{4 a^2 k^2 \sin ^4\left(\frac{t}{2}\right)+d^2 (a+b v)^2 \sin ^2(t)}}\right)^* \sqrt{4 a^2 k^2 \sin...

Homework Statement Compute the convolution y[n] = x[n] * h[n] if discrete signals: x[n] = \alpha^nu[n] h[n] = \beta^nu[n] Where \alpha \neq \beta. Homework Equations y[n] = \sum_{k=-\infty}^{\infty} h[n-k]x[k] The Attempt at a Solution I plugged the two equations into...

This is really a simplification of an equation. It is just very long and complex and I need advice. For ellipse center at the origin with tilt angle \tau, the distance from origin to the ellipse is \rho(\varsigma). It is given: \varsigma\;=\;\frac...

These are just some example equations: 60^x-36^x or 30^x-25^x where the x is raised to the power. How can (if possible) I simplify these equations?

Homework Statement \frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } } Homework Equations The Attempt at a Solution Wolfram Alpha somehow managed to simplify the equation to just simply 100. Here's my attempt: \frac { x+100 }{ 1+\frac { 100x }{ { 100 }^{ 2 } } } \\ =\frac...

Homework Statement solve the det 3 1 1 0 -4 5 0 -1 0 7 2 8 2 -1 0 3 Homework Equations The Attempt at a Solution I am trying to solve it and get a different answer each time so I am doing something I shouldn't obviously. Ok I am adding rows to other rows...

Homework Statement I was looking at a solution for a practise question and in the last step they simplified -[(0.02)^4]/[4(0.98)^4] to 1/(4*49^4) How do you do this without a calculator?

[(x2 - 4)(x2 + 3)1/2] - [(x2 - 4)2(x2 + 3)3/2] I understand the first half which comes out to... (x-2)(x+2)(x2 + 3)1/2 I have know idea how to start the second half. Thanks in advance.

This is related to logic circuits. How do I simplify this boolean algebra(logic) into its simplest expression? h = (abc + abd + acd + bcd)’ My first attempt would be to change it into product-of-sum. h = (abc)'(abd)'(acd)'(bcd)' and then what next?

(3/x-2) - (4/x+2) / (7/x2-4) I got it down to... -x+14/7 but the book is showing x-14/7

Hello, Could someone please help me simplify the equation: \frac{-1}{(c1+c2)} \cdot ln [(m1-m2)g-(c1+c2)v] = \frac{t}{(m1+m2)} - \frac{1}{(c1+c2)} \cdot ln[(m1-m2)g] (where c1, c2, m1, m2, g, are constants) so as to get: v = \frac{(m1-m2)g}{(c1+c2)} \cdot [ 1 - exp[\frac{-(c1+c2)t...

Well, this is a task for those who prepares to enter a university. According to the textbook this task is among the easiest ones. I managed to simplify this part of the (4b^4 + 4ab^2+a^2):(2b^2 + a) = 2b^2 + a. Well, I can't proceed any further. Could you give me a hint?

I have been studying algebra, and a good portion seems to be, getting really long equations to simple ones. My question is is there ever a time in any math where you wouldn't want to simplify? Assuming it isn't just the teacher not caring if you do.

Homework Statement So I'm following along with my physics book and I get to the point where Mg * abs(sin(θ) - cos(θ)) <= μMg * (cos(θ) + sin(θ) Next they say: If tan(θ) >= 1 then sin(θ) - cos(θ) <= μ(cos(θ) + sin(θ)) => tan(θ) <= (1+μ) / (1-μ) Homework Equations The Attempt at a...

Homework Statement simplify the expression: f(x) = x+1 - x^2/x+2, 1/x^2 -4 Homework Equations leaving the answer as a quadratic polynomial. 1. = 3x^2 + 4x + 4 2. = x^2-4x + 4 3. x^2 -4x - 4 4. 3x^2 +4x - 4 5. x^2 +4x - 4 6. 3x^2 -4x -4 The...

Simple difference quotient question. Function --> simplify answer Homework Statement I just don't understand this question! Here, I will take a picture of it. Can someone please explain how I answer these? Or even show me a website that shows how to do these? Its not in my review book...

Hello, Say I'm working with ∫ sqrt(1-cos(t)) dt I end up with a substitution of u = 1-cos(t) and dt = du/sin(t) sub back in: ∫ sqrt(u) / sin(t) du Still got a t in there ... hrrmmm So I go to wolfram alpha for some inspiration and 'show steps'...

Homework Statement u^2 --------------- u^2 - 4 Homework Equations I am told that this is equal to 1+ 4/u^2 - 4The Attempt at a Solution No clue how these two are related. Factor out a u^2/u^2? But that alters the denominator. My next that is partial fraction decomp. Am...

Homework Statement This is a sub problem, the whole problem is find interval of convergence and radius of convergence but the thing I am having trouble with is how to simplify this simplify the series 2*4*6*8*(2n)/2*4*6*8...(2n+2) Homework Equations The Attempt at a Solution...

question is... (ln(2x+1/(1-x)-4x+x/(1-x)+2x))/2 I start by simplifying and then finding the derivative...correct?

\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \\ \frac{1}{(\frac{x - 3}{x -...

Homework Statement ~AB+AB~c+ABC Homework Equations AB+A~B=A [b]3. The attempt at solution ~AB+A A+B

Consider the following: On a circle of radius 1, two points are marked: P1 and P2. Two lines are drawn from the center of the circle: one from the center to P1, the other from the center to P2. The angle between these two lines is \theta. One more line is drawn: from P1 directly...

Hi I was wondering if there is any way to simplify this expression or if it's already in its simplest form. Thank you in advance: (a^n+b^n)/(a+b)

Say we have a rational function P(x)=(x^2-3x-4)/(x-4)=[(x+1)(x-4)]/(x-4) I'm a little confused as to why the (x-4) doesn't cancel out. It graphs the same as y=x+1 for x≠4. I feel like I'm missing something from the order of operations.

Homework Statement ∫1/((√x)+x))dx Homework Equations The Attempt at a Solution I understand the calculus but not the algebra, it's been a while. How can I write f(x) differently to make the problem seem easier?

Homework Statement (x^{2}-x^{-1}+1)(x^{3}+2x-6)^{7} Homework Equations Chain Rule & Power RuleThe Attempt at a Solution (x^{3}+2x-6)^{6}[(x^{3}+2x-6)(2x+x^{-2})+7(3x^{2}+2)(x^{2}-x^{-1}+1)] This is the farthest I've gotten but when I do additional computation I do not arrive at the correct...

Homework Statement I'm trying to figure out the interval of convergence of the serie: \Sigma^{\infty}_{n=2} \frac{(-1)^{n}x^{n/2}}{nln(n)} Homework Equations The Attempt at a Solution The book states that the serie isn't a power serie, but a substitution can be used to...

Homework Statement Simplify e^(2n ln sin(pi/3)) Homework Equations The Attempt at a Solution I know that I can simplify to the form e^ln sin(π/3)^2n but I'm stuck there. I can't see how I could end up with the answer (3/4)^n, which is supposed to be the right answer.

hii guys i have a problem on simplifying this F(s) = X1(m1 s^2 + k) - KX2 0 = X2(m1 s^2 + k) - kx1 take x1 to have value x1= X2(m1 s^2 + k)/k F(s) = X2(m1 s^2 + k)/k . (m1 s^2 + k) - kX2 X2 [(m1 s^2 + k)^2 -k / k] now we cover m1 and k by 1 because in the question they have...

Homework Statement I want the simplify the following equation Homework Equations \frac{x}{{p}^{2}}+\frac{n-x}{{(1-p)}^{2}}, where p=\frac{x}{n}The Attempt at a Solution I got this \frac{{n}^{2}}{x}-\frac{{n}^{2}}{n-x}, I don't think this is the right answer.

Homework Statement Use fundamental identities to simplify the expression: (sinx)^2 - (cosx)^2 ____________________ (sinx)^2 - (sinx cosx)*note: it's a numerator and denominator. The underscore line is the fraction line. *note: The answer in the back of the book is "1 + cotx" but I would...

Homework Statement Simplify the expression Cos(6θ) Simplify means - the angle for all trigonometric functions in your answer is to be only θ. Simplify in terms of sines and cosines Simplify in terms of cosines only Simplify in terms of sines only Homework Equations Basic Trig Identities...