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
Look at the numerical coefficients of both sides.
Coefficient of $\displaystyle x^2$ on the LHS is 5, so belongs it to $\displaystyle a+b;$ coefficient of $\displaystyle x$ on the LHS is 5, so belongs it to $\displaystyle 2a+b;$ coefficient $\displaystyle 5$ on the LHS is 5, so belongs it to $\displaystyle 2b+c.$
After that, you'll get CaptainBlack's system, which is easy to solve.