# Math Help - Partial fraction decomposition

1. ## Partial fraction decomposition

hello,

i have a problem i am stuck on. i have figured it out till the very end but can not find the answer.here it is.

The Problem : Find the partial fraction decomposition.
(-x+10)/(x^2+x-12)

here is what i got from that problem.

(-x+10)/(x+4)(x-3) = (A/(x+4))+(B/(x-3))

(-x+10)=A(x-3)+B(x+4)

(-x+10)=Ax-3A+Bx+B4

-1=A+B

10= (-3a)+(b4)

What is A and B so (A/(x+4))+(B/(x-3)) = (-x+10)/(x+4)(x-3)

Thank you.

2. Originally Posted by OnMyWayToBeAMathProffesor
hello,

i have a problem i am stuck on. i have figured it out till the very end but can not find the answer.here it is.

The Problem : Find the partial fraction decomposition.
(-x+10)/(x^2+x-12)

here is what i got from that problem.

(-x+10)/(x+4)(x-3) = (A/(x+4))+(B/(x-3))

(-x+10)=A(x-3)+B(x+4)

(-x+10)=Ax-3A+Bx+B4

-1=A+B

10= (-3a)+(b4)

What is A and B so (A/(x+4))+(B/(x-3)) = (-x+10)/(x+4)(x-3)

Thank you.

so i guess you are having trouble solving the simultaneous equations?

here's another approach

$-x + 10 = A(x - 3) + B(x + 4)$

Let $x = 3 \implies -3 + 10 = 7B$
Let $x = -4 \implies 4 + 10 = -7A$

there you have your A and B

the method you were attempting was the equating coefficients method, i don't see the problem you have, the only thing left for you to do is to solve the simultaneous equations