Let A and B be real numbers such that A/(x - 5) + B/(x + 1) = (12x + 22)/(x^2 - 4x - 5). What is A+B?
+129845 Note that x^2 - 4x - 5 = ( x - 5) ( x + 1)
Multiply through by these two factors and we get
12x + 22 = A( x + 1) + B ( x -5) simplify
12x + 22 = (A + B)x + ( A - 5B) equating terms we have
A + B = 12 → B = 12 - A (1)
A - 5B = 22 (2)
Sub (1) into (2)
A - 5 ( 12 - A) = 22
A - 60 + 5A = 22
6A = 82
A = 82/6 = 41/3
And
B = 12 - 41/3 = 36/3 - 41/3 = - 5 / 3
A + B = 36/3 = 12
