Question

[b]Упростить[/b]
$\frac{a^3+b^3}{(a+b)(a^2-b^2)}+\frac{2b}{a+b}$

Answer 1

Решение

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

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

$\frac{a^{2}-ab+b^{2}}{a^{2}-b^{2}}+\frac{2b}{a+b}$

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

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

$\frac{a^{2}-ab+b^{2}+2ab-2b^{2}}{a^{2}-b^{2}}$

Ответ

$\frac{a^{2}+ab-b^{2}}{a^{2}-b^{2}}$