Find constants A and B such that \(\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\) for all x such that \(x\neq -1\) and \(x\neq 2\). Give your answer as the ordered pair (A,B).

Lightning
Aug 18, 2018

#1**+3 **

\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}

\(\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\\ A(x+1)+B(x-2)=x+7\\ Ax+Bx=x \qquad A-2B=7\\ A+B=1 \qquad A=7+2b\\ 7+2B+B=1\\ 7+3B=1\\ 3B=-6\\ B=-2\\ A=3\\~\\ check\\ 3(x+1)-2(x-2)=x+7 \quad great \)

answer (3,-2)

Melody
Aug 18, 2018

#3**+1 **

That is not a problem Alan

Maybe 2 answers are better than one and it certainly is not your fault if Lightning double posted.

Melody
Aug 18, 2018