Question

Sabendo que a / 2x + 1 + b / 2x – 1 = 2x + 5 / 4x² - 1, o valor de a + b é igual a:

– 2 (B) – 1 (C) 1 (D) 2 (E) 3

Answer 1

Explicação passo-a-passo:

$\sf \dfrac{a}{2x+1}+\dfrac{b}{2x-1}=\dfrac{2x+5}{4x^2-1}$

$\sf \dfrac{a\cdot(2x-1)+b\cdot(2x+1)}{(2x+1)\cdot(2x-1)}=\dfrac{2x+5}{4x^2-1}$

$\sf \dfrac{2ax-a+2bx+b}{4x^2-1}=\dfrac{2x+5}{4x^2-1}$

$\sf \dfrac{(2a+2b)x-a+b}{4x^2-1}=\dfrac{2x+5}{4x^2-1}$

$\sf (2a+2b)x-a+b=2x+5$

Devemos ter:

$\sf 2a+2b=2$

$\sf 2\cdot(a+b)=2$

$\sf a+b=\dfrac{2}{2}$

$\sf a+b=1$

Letra C