How Do You Apply the Quotient Rule to Differentiate (x-1)^2/(x+1)^2?

[Nitrate]

Homework Statement

a) Differentiate y=((x-1)/(x+1))^2

b (non calculus simplification question):
How would i simplify 10(5x+3)(5x-1)+5(5x-1)^2 to get 25(5x-1)(3x+1)
should i expand all terms then combine and factor?

Homework Equations

The Attempt at a Solution

a) i tried using the quotient rule but kept ending up with missing terms...
from the answer key i know that the answer is (4(x-1))/(x+1)^3
but i can't get that for the life of me...

 

[iRaid]

Chain rule on this simplifies it a lot.. (if you know it?)

y=u^{2}

u=\frac{x-1}{x+1}


EDIT: Just in case you don't knnow, take the derivative of y and u then do the following:

\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}

 

[Nitrate]

Chain rule on this simplifies it a lot.. (if you know it?)

y=u^{2}

u=\frac{x-1}{x+1}

i do
however I've never really learned it using substitutions.
would i bring up the (x+1)^2 to the top, so that the equation becomes (x-1)^2(x+1)^-2?
or would that further complicate things

 

[iRaid]

i do
however I've never really learned it using substitutions.
would i bring up the (x+1)^2 to the top, so that the equation becomes (x-1)^2(x+1)^-2?
or would that further complicate things

I editted my post, maybe that will help you