+280 Find constants A and B such that \(\frac{2x + 11}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\)for all x such that \(x\neq -1\) and \(x\neq 2\).
+129895 x^2 - x - 2 = (x - 2) ( x + 1)
Multiply through by the factorization and we get
2x + 11 = A(x + 1) + B( x -2)
2x + 11 = (A + B)x + (A - 2B)
Equating terms
A + B = 2 → B = 2 - A (1)
A - 2B = 11 (2)
Sub (1) into (2)
A - 2 ( 2 -A) = 11
A - 4 + 2A = 11
3A = 15
A = 5
B = 2 - 5 = -3
