Question

a^2-b^2 разделить на а-b минус a^3-b^3 разделить на a^2-b^2

Answer 1

$frac{a^2-b^2}{a-b}-frac{a^3-b^3}{a^2-b^2}=\=frac{(a-b)(a+b)}{(a-b)}-frac{(a-b)(a^2+ab+b^2)}{(a-b)(a+b)}=\=a+b-frac{(a^2+ab+b^2)}{a+b}=\=frac{a^2+2ab+b^2-a^2-ab-b^2}{a+b}=\=frac{ab}{a+b}$

Answer 2

$frac {a^2-b^2}{a-b}-frac {a^3-b^3}{a^2-b^2}=frac {(a-b)(a+b)}{a-b}-frac {(a-b)(a^2+ab+b^2)}{(a-b)(a+b)}= \ \ = (a+b)-frac {a^2+ab+b^2}{a+b}= frac {(a+b)^2}{a+b}-frac {a^2+ab+b^2}{a+b}=frac {a^2+2ab+b^2-a^2-ab-b^2} {a+b}=\ \ = boxed {frac {ab}{a+b}}$