Question

Find any points of discontinuity for the rational function.
y=(x+2)(x-2)(x+4)/(x-1)(x-8)
please help me

Answer 1

Rational functions have discontinuities precisely at the zeros of the denominator. It looks like you meant to type
\[y=\frac{(x+2)(x-2)(x+4)}{(x-1)(x-8)},\]
so you just need to find the zeros of f(x)=(x-1)(x-8).

Answer 2

really? so x=1 and x=8?

Answer 3

Yep.

Answer 4

wow thats easy thanx man

Answer 5

It's worth noting that if the zero occurs in both the numerator and denominator the same number of times, then it's removable (just cancel the factors out). In this case, they're both infinite discontinuities because the numerator is nonzero at both 8 and 1.