Find the value of k
(x^(3)+1)/(x^(2)-3x+2)=(kx-5)+[(7x-5)/((x-1)(x-2))]
(x^(3)+1)/(x^(2)-3x+2)=(kx-5)+[(7x-5)/((x-1)(x-2))]
(x^3 + 1)/((x-1)(x-2)) = (kx - 5) + (7x-5)/((x-1)(x-2))
multiply both sides by (x-1)(x-2)
x^3 + 1 = (kx-5)(x-1)(x-2) + 7x-5
x^3 + 1 = kx^3 + ....
the only x^3 terms are 1x^3 on the left and kx^3 on the right, so k = 1