There are values A and B such that (Bx-11) / (x^2-7x+10) = A/(x-2) - 3/(x-5).
Find A+B
+128475 Note that ( x - 2) ( x - 5) = x^2 - 7x + 10
So....if we multiply both sides both the equation by the polynomial we get that
(B x - 11) = A(x - 5) - 3(x - 2) simplify
Bx - 11 = Ax - 5A - 3x + 6
Bx -11 = (A - 3)x + ( 6- 5A )
This implies that
B = A - 3 ⇒ A = B + 3 (1)
-11 = 6 - 5A (2)
Sub (1) into (2)
-11 = 6 - 5( B + 3)
-17 = -5B - 15
-2 = -5B
B = 2/5
A = 2/5 + 3 = 17/5
A + B = 17/5 + 2/5 = 19/5
