solving partial fractions, such as (x+22)/((x+4)(x-2)

Question

i need to find the answers to this and i am lost....

Answer 1

Given expression (x+22)/(x+4)(x-2)

x+22 = A(x-2)+B(x+4)

x+22 = Ax-2A+Bx+4B

Equating the x coefficients.

A+B = 1 ---> (1)

Equating constants.

-2A+4B = 22 ---> (2)

Multiple to each side of equation (1) by 2.

2A+2B = 2 ---> (3)

To eliminate the A value add the equations (3)&(2).

2A+2B = 2

-2A+4B = 22

___________

6B = 24

Divide to each side by 6.

B = 4

Substiute theB value in (1).

A+4 = 1

Subtract 4 from each side.

A = -3

Partial fractions of