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
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.
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.