+817 I need help with algebra
Find constants $A$ and $B$ such that
\[\frac{2x + 11 - x - 13}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\]
for all ${}x$ such that $x\neq -1$ and $x\neq 2$.
+129771 Note that x^2 - x - 2 can be factored as (x - 2) ( x + 1)
Multiply the equation through by this factorization and we get
2x + 11 - x - 13 = A(x + 1) + B ( x -2)
x - 2 = A(x + 1) + B ( x -2)
1x - 2 = (A + B)x + A - 2B equting coefficients on both sides of the eqution we have
1 = A + B
-2 =A - 2B
Multiply the second equation through by -1
1 = A + B
2 = -A + 2B add these
3 = 3B
So B = 1
And
A + B = 1
So A = 0
