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)

First subtract 10 from both side
y^2+6y-16=0
(y+8)(y-2)=0
-8 and 2