Question

decompose into partial fractions (3x+15)/(x+4)²​

Answer 1

SOLUTION

Your input: perform the partial fraction decomposition of 3x+15(x+4)2

The form of the partial fraction decomposition is

3x+15(x+4)2=Ax+4+B(x+4)2

Write the right-hand side as a single fraction:

3x+15(x+4)2=(x+4)A+B(x+4)2

The denominators are equal, so we require the equality of the numerators:

3x+15=(x+4)A+B

Expand the right-hand side:

3x+15=xA+4A+B

Collect up the like terms:

3x+15=xA+4A+B

The coefficients near the like terms should be equal, so the following system is obtained:

{A=34A+B=15

Solving it ,

we get that A=3, B=3

Therefore,

3x+15(x+4)2=3x+4+3(x+4)2

Answer: 3x+15(x+4)2=3x+4+3(x+4)2