Find constants A and B such that $\frac{x + 2}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}$ for all x such that $x \neq -1$ and $x \neq 2$. Give your answer as the ordered pair (A,B).
+526 x+2x2−x−2=x+2(x−2)(x+1)=Ax−2+Bx+1
Multiplying by (x - 2)(x + 1) both sides,
A(x+1)+B(x−2)=x+2
Put x = -1 ⇒ -3B = 1
B = -1/3
Put x = 2 ⇒ 3A = 4
A = 4/3
Thus the answer is (43,−13).
+526 x+2x2−x−2=x+2(x−2)(x+1)=Ax−2+Bx+1
Multiplying by (x - 2)(x + 1) both sides,
A(x+1)+B(x−2)=x+2
Put x = -1 ⇒ -3B = 1
B = -1/3
Put x = 2 ⇒ 3A = 4
A = 4/3
Thus the answer is (43,−13).
