Hello i need to solve for x in the this problem to prove the range

y= sqrt((1-x^{2})/(1+x^{2}))

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- Sep 26th 2012, 08:30 AMchizmin10help with algebra withing calculus problem
Hello i need to solve for x in the this problem to prove the range

y= sqrt((1-x^{2})/(1+x^{2})) - Sep 26th 2012, 08:37 AMMarkFLRe: help with algebra withing calculus problem
We are given:

$\displaystyle y=\sqrt{\frac{1-x^2}{1+x^2}}$

To remove the radical, square both sides:

$\displaystyle y^2=\frac{1-x^2}{1+x^2}$

Now multiply through by $\displaystyle 1+x^2$:

$\displaystyle y^2+x^2y^2=1-x^2$

Arrange with terms involving $\displaystyle x$ on the left, and the rest on the right:

$\displaystyle x^2+x^2y^2=1-y^2$

Factor the left side:

$\displaystyle x^2(1+y^2)=1-y^2$

Can you proceed from here? - Sep 26th 2012, 08:44 AMchizmin10Re: help with algebra withing calculus problem
Hmmm, im sorry you'll have to excuse my lack of knowledge. I haven't had math courses of any kind for several years. What is the final step you did factoring the left side. How did you completely get rid of one x^2

- Sep 26th 2012, 08:56 AMchizmin10Re: help with algebra withing calculus problem
Oh nvm i got it. So then would you divide out the (1+y^2) and then take the square root of the whole thing?

- Sep 26th 2012, 09:18 AMMarkFLRe: help with algebra withing calculus problem
Yes, exactly! :)

- Sep 26th 2012, 09:39 AMchizmin10Re: help with algebra withing calculus problem
awesome thanks for the help!