Thread: Partial fractions

Hi i got the following:

5x^2 + 5x + 5 = (Ax+B)(x+2) + C(x^2 + 1)

Now i got C = 3
But confused how to get A and B
I know you have to equate both sides for x^2
so:

5=[confused]

Originally Posted by taurus

Hi i got the following:

5x^2 + 5x + 5 = (Ax+B)(x+2) + C(x^2 + 1)

Now i got C = 3
But confused how to get A and B
I know you have to equate both sides for x^2
so:

5=[confused]

You expand the left hand side and collect terms of like order in x, then
you equate coefficients of like powers of x on each side of the equation
to give a set of three simultaneous equations in A, B and C.

Doing this we have:

5x^2 + 5x + 5 = (A+B)x^2 + (2A+B)x + (2B+C)

so we have:

..A +. B ..... = 5
2A + .B ..... = 5
...... 2B + C = 5

Which you now solve.

RonL

5x^2 + 5x + 5 = (A+B)x^2 + (2A+B)x + (2B+C)

still confused how you got that?

Look at the numerical coefficients of both sides.

Coefficient of on the LHS is 5, so belongs it to coefficient of on the LHS is 5, so belongs it to coefficient on the LHS is 5, so belongs it to

After that, you'll get CaptainBlack's system, which is easy to solve.

but how did you get these:

(A+B)x^2 + (2A+B)x + (2B+C)

ok i get it, but now how do i solve for A and B?