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 \((A,B)\).
+36916 Cross multiply the right side to get
a(x+1) + b (x-2)
(x^2 -x-2) equate the L and R numerators
a (x+1) + b(x-2) = x+7
ax + a + bx -2b = x + 7
from this we can get ax + bx = x and a -2b = 7
a+ b =1 a - 2b= 7 multiply red equation by -1 and add to second equation to get
-3b = 6
b = -2 then a = 3
