Hello i need to solve for x in the this problem to prove the range
y= sqrt((1-x^{2})/(1+x^{2}))
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?
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