Question

3- Dada a igualdade, $\frac{5x - 3}{x^{2}- 2x -3 } = \frac{A}{x - 3} + \frac{B}{x + 1}$ , determine o valor de A e B

Answer 1

$\large\boxed{\begin{array}{l}\rm\dfrac{5x-3}{x^2-2x-3}=\dfrac{5x-3}{(x-3)\cdot(x+1)}\\\\\rm\dfrac{5x-3}{(x-3)\cdot(x+1)}=\dfrac{A}{x-3}+\dfrac{B}{x+1}\\\\\rm A=\dfrac{5x-3}{x+1}\bigg|_{x=3}=\dfrac{5\cdot3-3}{3+1}\\\\\rm A=\dfrac{12}{4}=3\\\\\rm B=\dfrac{5x-3}{x-3}\bigg|_{x=-1}=\dfrac{5\cdot(-1)-3}{-1-3}\\\\\rm B=\dfrac{-8}{-4}=2\end{array}}$