find domain express in interval notation x7x2x42Solutionx7x

find domain express in interval notation : x+7/x^2+x-42

(x+7)/(x²+x-42)

First we have to factor the denominator

(x+7)/(x+7)(x-6)

The rational function is undefined when the bottom is zero

And here the points which make the denominator zero is

x+7=0 and x-6=0

x=-7 and x=6

Therefore the given rational expression is undefined at x=-7 and x=6

Hence the domain is all the real values besides x=-7 and x=6

And the interval notation is (-infinity,-7) union (-7,6) union (6,infinity)