Need algebra to simplify/solve an equation

the equation that i need to simplify first is ((x^2-1)^1/2 -(x^2-1)^-1/2 (2-x^2)) / (x^2-1)= 0

after i move the negative power, im not exactly sure what to do. I would multiply by the reciprical to get rid of the fration in the numerator but the 1/2 exponent makes things difficult. help is much appreciated!

Re: Need algebra to simplify/solve an equation

Do you mean simplify or solve?

Is this the equation?

$\displaystyle \displaystyle \frac{ \frac{1}{\sqrt{x^2-1}} - \frac{(2-x^2)}{\sqrt{x^2-1}} }{x^2-1} = 0$

if so, $\displaystyle x\neq 1,-1$

$\displaystyle \displaystyle \frac{ \frac{1- (2-x^2)}{\sqrt{x^2-1}} }{x^2-1} = 0$

$\displaystyle \displaystyle \frac{ \frac{1- 2+x^2}{\sqrt{x^2-1}} }{x^2-1} = 0$

$\displaystyle \displaystyle \frac{ \frac{-1+x^2}{\sqrt{x^2-1}} }{x^2-1} = 0$

Now you can multiply both sides by $\displaystyle x^2-1$

$\displaystyle \displaystyle \frac{-1+x^2}{\sqrt{x^2-1}} = 0$

Multiply both sides by $\displaystyle \sqrt{x^2-1}$ and you'll find $\displaystyle x=1,-1$ , but can it?

Re: Need algebra to simplify/solve an equation

Re: Need algebra to simplify/solve an equation

yes thats basically the right equation. the answer key says the answer is x = plus or minus the squareroot of 3/2. and i have no idea how that can work out...

Re: Need algebra to simplify/solve an equation

I think the correct interpretation is:

$\displaystyle \dfrac{\sqrt{x^2-1}-\dfrac{2-x^2}{\sqrt{x^2-1}}}{x^2-1}=0$

$\displaystyle \dfrac{\dfrac{(\sqrt{x^2-1})^2-(2-x^2)}{\sqrt{x^2-1}}}{x^2-1}=0$

$\displaystyle \dfrac{x^2-1-2+x^2}{\sqrt{x^2-1}(x^2-1)}=0$

$\displaystyle \dfrac{2x^2-3}{\sqrt{x^2-1}(x^2-1)}=0$

Which is 0 if

$\displaystyle 2x^2-3=0 \Rightarrow x=\pm \sqrt{\dfrac{3}{2}}$

Re: Need algebra to simplify/solve an equation

Quote:

Originally Posted by

**Victalam** yes thats basically the right equation....

basically?