Question

(a^2-b^2):(a^-1+b^-1)

Answer 1

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

Answer 2

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