Find any points of discontinuity for the rational function y = x - 8/x² + 5x - 6

Solution:

Given function:

y = (x - 8)/(x² + 5x - 6)

In order to find our points of discontinuity, we need to factor the polynomial in the bottom.

When we get the two binomials, we'll set each of them equal to 0.

y = (x + 8)/(x + 6)(x - 1)

x + 6 = 0

x = -6

x - 1 = 0

x = 1

When x = -6, y = undefined

When x = 1, y = undefined

Therefore, the asymptotes at x = -6 and x = 1 hence they are the points of discontinuity.

Find any points of discontinuity for the rational function y = x - 8/x² + 5x - 6

Summary:

On the asymptotes x = 1,x = -6 there are points of discontinuity for the rational function y = x - 8/x² + 5x - 6.