David K. answered • 01/15/21

Mathematics tutor for middle school to graduate students

Graphically I see an asymptotes at x=-1,2,4

From the equation y = (x + 5) / (x + 1) - ((x + 3) (x - 2)) / ((x - 4) (x + 1)) - 1 / (x - 2)

We know vertical asympotes occur where the denominator is zero. So x + 1 = 0 when x=-1. Remember that when x gets close to -1 the fraction (x + 5) / (x + 1) becomes large.

Also ((x - 4) (x + 1)) = 0 when either (x - 4)= 0 or (x + 1)=0. So when x=4 or -1.

(x - 2) = 0 when x=2.

For part b. there is a vertical asymptote at x=-1. There may be a typo in your equation.