Question

Decompose into partial fractions: 12/x^2-9

Answer 1

2/ (x -3) - 2/ (x + 3)

Answer 2

that\s 12/(x+3)(x-3) right?

so your partial fraction is A/x+3 + B/x-3 correct?

so 12/(x+3)(X-3) = a/(X+3) + B/x-3

multiply both sides by (x+3)(x-3)...the LCD

that gives you 12 = A(x-3) + B(x+3)

expand...

12 = Ax - 3A + Bx +3B

now use gaussian method (if you're familiar with it)

COEFFICIENTS OF x

0 = A + B

COEFFICIENT OF CONSTANT

12 = -3a + 3B
4 = B -A

system of linear eq...

B-A = 4
B + A = 0
2b =4

b = 2
so a = -2

so your equation is

2/x+3 - 2/x-3

do you understand?

Answer 3

wow. Yes. Thanks so much lgbasallote!!!