Question

Упростите выражение. Помогите!

Answer 1

$( frac{1}{a^2}+ frac{1}{b^2}+ frac{2}{a+b}cdot( frac{1}{a}+ frac{1}{b})): (frac{a+b}{ab})^2=1$

$boxed{1} frac{1}{a}+ frac{1}{b} = frac{a+b}{ab}\\ boxed{2} frac{2}{a+b}cdot frac{a+b}{ab}= frac{2}{ab}\\ boxed{3} frac{1}{a^2}+ frac{1}{b^2}+ frac{2}{ab}= frac{b^2+a^2+2ab}{a^2b^2}= frac{(a+b)^2}{a^2b^2}\\ boxed{4} frac{(a+b)^2}{a^2b^2}: (frac{a+b}{ab})^2= frac{(a+b)^2}{a^2b^2}cdot frac{a^2b^2}{(a+b)^2} =1$