Write the partial fraction decomposition of the rational expression. 18x^2-68x+24/x (x-2) (x-4)

= A/x + B / (x - 2) + C / (x - 4)

To find A, multiply the expression by x and evaluate at x=0.

... A = 24 / ((-2) * (-4)) = 3

To find B, multiply the expression by x-2 and evaluate at x=2.

... B = (18*2^2 - 68*2 + 24) / (2 * (2-4)) = - 40/-4 = 10

To find C, multiply the expression by x-4 and evaluate at x=4.

... C = (18*4^2 - 68*4 + 24) / (4 (4 - 2)) = 40/8 = 5

The partial fraction decomposition is

... = 3/x + 10 / (x - 2) + 5 / (x - 4)