# help with algebra withing calculus problem

• Sep 26th 2012, 08:30 AM
chizmin10
help with algebra withing calculus problem
Hello i need to solve for x in the this problem to prove the range

y= sqrt((1-x2)/(1+x2))
• Sep 26th 2012, 08:37 AM
MarkFL
Re: 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 AM
chizmin10
Re: 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 AM
chizmin10
Re: 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 AM
MarkFL
Re: help with algebra withing calculus problem
Yes, exactly! :)
• Sep 26th 2012, 09:39 AM
chizmin10
Re: help with algebra withing calculus problem
awesome thanks for the help!