Respostas

  • Usuário do Brainly
2014-08-31T06:09:08-03:00
Observe que, a^2-b^2=(a+b)(a-b) e a^2+2ab+b^2=(a+b)^2.

Assim, \text{mmc}(a^2-b^2,a^2+2ab+b^2)=(a+b)^2(a-b)

Deste modo:

\dfrac{x+1}{a^2-b^2}-\dfrac{x-1}{a^2+2ab+b^2}=\dfrac{x+1}{(a+b)(a-b)}-\dfrac{x-1}{(a+b)^2}

\dfrac{(a+b)(x+1)-(x-1)(a-b)}{(a+b)^2(a-b)}=\dfrac{ax+bx+a+b-ax+bx+a-b}{(a+b)^2(a-b)}

\dfrac{(a+b)(x+1)-(x-1)(a-b)}{(a+b)^2(a-b)}=\dfrac{2bx+2a}{(a+b)^2(a-b)}

\dfrac{x+1}{a^2-b^2}-\dfrac{x-1}{a^2+2ab+b^2}=\dfrac{2(bx+a)}{(a+b)^2(a-b)}
A minha dúvida é na parte do MMC