Find the value of A + B − C for which (x^2t+12x+12) / ( x(x-2)(x+2) )=

Question

A/x + B/(x-2)+ C/(x+2)
a) 1
b) 3
c) 7
d) -7

Answer 1

just put everything over a common denominator:
A/x + B/(x-2)+ C/(x+2)
= (A(x^2-4) + B(x^2+2x) + C(x^2-2x))/(x(x-2)(x+2))
Now you want that to be identical to (x^2+12x+12)/(x(x-2)(x+2))
That means that
A(x^2-4) + B(x^2+2x) + C(x^2-2x) = x^2+12x+12
(A+B+C)x^2 + (2B-2C)x + (-4A) = x^2+12x+12
So, now you know that
A+B+C = 1
2B-2C = 12
-4A = 12
Now just crank it out.