Question

(ufmg) considere o conjunto de todos os valores de a e b para os quais a expressao M = a/b+a +b/a-b + 2ab/a2-b2

Answer 1

$M= \frac{a}{(a+b)} + \frac{b}{(a-b)} + \frac{2ab}{a^{2}-b^{2}} \\M= \frac{a}{(a+b)} + \frac{b}{(a-b)} + \frac{2ab}{(a+b)(a-b)}\\M= \frac{a(a-b)+b(a+b)+2ab}{(a+b)(a-b)} \\M= \frac{a^{2}-ab+ab+b^{2}+2ab}{(a+b)(a-b)}\\ M= \frac{a^{2}+2ab+b^{2} }{(a+b)(a-b)}\\ M= \frac{(a+b)^{2}}{(a+b)(a-b)}\\M= \frac{a+b}{a-b} \\\\Espero~ter~ajudado.$