# Thread: Need help with partial fraction

1. ## Need help with partial fraction

I get stuck at the ((Ax+B)/(x^2+1)) + ((Cx+D)/(x^2+2)) part.

How exactly do we solve for these variables A, B, C, and D? If I plug in zero the equation would become:

3x^3 - x^2 + 6x - 4 = (Ax+B)(x^2+2) + (Cx+D)(x^2+1)

3(0)^3 - (0)^2 + 6(0) - 4 = (A(0)+B)((0)^2+2) + (C(0)+D)((0)^2+1)

That would leave me with: -4 = 2B + D.

I have tried multiplying it out and setting it equal to the coefficient such as this:

A + C = 3
B + D = -1
2A + C = 6
2B + D = -4

But to no avail. Please help me figure out how to solve for these variables. Thanks in advance.

2. You should remember simultaneous equations from your algebra classs

So you have

$\displaystyle 2A+C=6$....(I)

$\displaystyle A+C=3$......(II)

Subtract Equation(II) from Equation (I), and you'll have:

$\displaystyle 2A-A+C-C = 6-3 \implies A=3$,

And with $\displaystyle A =3$, you can find the value of C, which is .....

Then Use the same approach in the equations involving B and D.

$\displaystyle B + D = -1$

$\displaystyle 2B + D = -4$