Question

упростите выражение

Answer 1

$( frac{a}{b} + frac{b}{a} -2)* frac{1}{a-b} =( frac{a*a}{ab} + frac{b*b}{ba} - frac{2}{1} )* frac{1}{a-b} = (frac{a^2}{ab} + frac{b^2}{ab} - frac{ab*2}{ab} )* frac{1}{a-b} =$
$( frac{a^2}{ab} + frac{b^2}{ab} - frac{2ab}{ab} )* frac{1}{a-b} = frac{a^2-2ab+b^2}{ab} * frac{1}{a-b} = frac{(a-b)^2}{ab} * frac{1}{a-b} = frac{a-b}{ab} .$