Write an equation for a rational function with: vertical asymptotes at x = 6 and x = 4 and x intercepts at x = 5 and x = -2y intercept at 8

Asolution:     ======explanation: for vertical asymptotes to be at x = 6 and x = 4, the factors (x-6) and (x-4) must be in the denominator of a rational function of the form p(x)/q(x)  to facilitate a division by zero.for x-intercepts to be at x = 5 and x = -2, the factors (x-5) and (x+2) must be in the numerator of a rational function of the form  p(x)/q(x)  so that those values will result in the numerator being 0. 0 divided by any nonzero number is 0.we would have some coefficient to determine. so our function currently looks like this:     where a is a constant to be determined.the y-intercept occurs at x = 0. if we want a y-intercept of 8, the value of the function (represented by y) must be equal to 8 when x = 0. this gives us a single variable equation to solve.    therefore, an equation of a rational function that satisfies these conditions is