Perform partial fraction decomposition for the following rational functions. After multiplying through by the denomina- tor of the left hand side, we have. Solution: the denominator factors into x(x 1). Both x and x 1 are linear terms of degree 1. Thus the general form of the solution will be. After multiplying through by x(x 1) we have: 11x 10 = a(x 1) + bx. 10 = a (the equation from x) (the equation from 1) From this a = 10 and b = 1. Plugging 0 into this equation shows us that. Plugging 4 into this equation shows us that. 1 x 1 ahere we equate the coe cients of the x terms and the coe cients of the constant terms to come up with two equations. Solution: observe that x2 + 1 is an irre- ducible quadratic since b2 4ac = 02 4 1 . Thus the general form of the partial fraction decomposition is.