how do you find a partial fraction decomposition of -22x/ 3x^2 +7x-6

Question

how do you find a partial fraction decomposition of  -22x/ 3x^2 +7x-6

owlfred · Answer

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

anonymous · Answer

Could you be more specific?
Is it 22x/ (3x^2 +7x -6)? or is it the way you wrote it? Because this will have a huge effect on the answer :)

myininaya · Answer

$$\frac{-22x}{3x^2+9x-2x-6)}=\frac{-22x}{3x(x+3)-2(x+3)}=\frac{-22x}{(3x-2)(x-3)}=\frac{A}{3x-2}+\frac{B}{x-3}$$

myininaya · Answer

$$-22x=A(x-3)+B(3x-2)$$

myininaya · Answer

-22x=Ax+3Bx-3A-2B

annon · Answer

myininaya u beet me to the punch lol

myininaya · Answer

22x=(A+3B)x+(-3A-2B)
A+3B=22
-3A-2B=0

myininaya · Answer

A=22-3B
-3(22-3B)-2B=-66+9B-2B=-66+7B=0
7B=66
B=66/7
so
A=22-3(66/7)=-44/7
so
$$\frac{-22x}{3x^2+7x-6}=\frac{\frac{-44}{7}}{3x-2}+\frac{\frac{66}{7}}{x-3}=\frac{-44}{7(3x-2)}+\frac{66}{7(x-3)}$$

myininaya · Answer

im sorry annon i just realized u said something
you can check my work if you want