1. 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]

2. 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

3. 5x^2 + 5x + 5 = (A+B)x^2 + (2A+B)x + (2B+C)

still confused how you got that?

4. Look at the numerical coefficients of both sides.

Coefficient of $x^2$ on the LHS is 5, so belongs it to $a+b;$ coefficient of $x$ on the LHS is 5, so belongs it to $2a+b;$ coefficient $5$ on the LHS is 5, so belongs it to $2b+c.$

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

5. but how did you get these:

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

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