# Need help with partial fraction

• Feb 10th 2011, 06:04 PM
florx
Need help with partial fraction
Attachment 20743

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.
• Feb 10th 2011, 06:46 PM
harish21
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\$