What is the hole in the graph of this rational expression?? Please correct my answer/ check my answer

Question

#(x^2-4)/((x+2)(x^2-49)#
The numerator is in parenthesis
My answer: #-4/5# or #-4/9# or #-4/(5(9)#

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Answer 1 · 2018-04-14T03:34:02

The hole in the graph occurs when #x=-2#

The hole in a rational function is created when a factor in the numerator and denominator are the same.

#(x^2-4)/((x+2)(x^2-49)) " "# Factor to get

#((x-2)(x+2))/((x+2)(x-7)(x+7)) " "# The factor #(x+2)# will cancel.

This means the hole will occur when #x+2=0# or #x=-2#