−=?
6 (x^{2}−y^{2}) x^{−2}−y^{−2}
I was thinking along the lines of -6(x^{2}-y^{2})/ 1/x^{2}-y^{2 }-> -6(x^{2}-y^{2}) *x^{2}-y^{2 }-> -6(x^{2}-y^{2})^{2} but that's wrong
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
Instead this should be
$\displaystyle x^{-2}-y^{-2} = \frac{1}{x^2}-\frac{1}{y^2}$
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 ...