# Thread: Solve the complex fraction

1. ## Solve the complex fraction

 6 (x2−y2) x−2−y−2
=?

I was thinking along the lines of -6(x2-y2)/ 1/x2-y2 -> -6(x2-y2) *x2-y2 -> -6(x2-y2)2 but that's wrong

2. ## Re: Solve the complex fraction

Are you just trying to simplify the fraction rather than solve it?

Also is your equation supposed to be this?
$\displaystyle \frac{6(x^2-y^2)}{x^{-2}-y^{-2}}$

From your attempt it appears that you are assuming $\displaystyle x^{-2}-y^{-2} = \frac{1}{x^2-y^2}$ but this is incorrect

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

3. ## Re: Solve the complex fraction

I believe you mean simplify, rather than solve ...

Denominator ...

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

Now, numerator divided by denominator ...

$\displaystyle 6(x^2-y^2) \div \frac{y^2-x^2}{x^2y^2} = ?$

Finish it ...

4. ## Re: Solve the complex fraction

You're kinda close; hint:
Denominator = 1/x^2 - 1/y^2 = -(x^2 - y^2) / (x^2 y^2)
Notice that x^2-y^2 will cancel out...

Leaving you the satisfaction of wrapping it up