first, "partial differentiation" is something completely different. you are not differentiating here at all. in fact, this technique is usually used to aid in integration.

here's a start:

...........(look up the partial fraction decomposition to see how we got this)

multiply both sides by

there are several ways to proceed here. one is to pick x-values that cause all but one variable to be wiped out and solve for each variable one by one. for example, if we plug in x = 0, we get

.........and we've found B. do a similar trick to find A and C

another way is to expand the right side, group the like powers of x and equate coefficients. lets find B again using this method

B is the constant term on the right, so it must be the same as the constant term on the left to have equality, thus, again, B = 75

now finish up with the method of your choice