2/a-2/b / 1/a^2 - 2/b^2 this is a division problem dealing with fractions and variables ?

Feb 23, 2017

$\frac{\frac{2}{a} - \frac{2}{b}}{\frac{1}{a} ^ 2 - \frac{2}{b} ^ 2} = \frac{2 a b \left(b - a\right)}{{b}^{2} - 2 {a}^{2}}$

Explanation:

(2/a-2/b)/(1/a^2-2/b^2

= $\frac{\frac{2 b - 2 a}{a b}}{\frac{{b}^{2} - 2 {a}^{2}}{{a}^{2} {b}^{2}}}$

= $\frac{2 b - 2 a}{a b} \times \frac{{a}^{2} {b}^{2}}{{b}^{2} - 2 {a}^{2}}$

= $\frac{2 \left(b - a\right)}{a b} \times \frac{a b \times a b}{{b}^{2} - 2 {a}^{2}}$

= $\frac{2 \left(b - a\right)}{\cancel{a b}} \times \frac{\cancel{a b} \times a b}{{b}^{2} - 2 {a}^{2}}$

= $\frac{2 a b \left(b - a\right)}{{b}^{2} - 2 {a}^{2}}$