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The graph of which of the following rational equations has a hole

A. f(x) = (x2 + 5x + 4) / (x2 + x - 12)

B. f(x) = (x2 - 2x + 1) / (x2 + 7x -15)

C. f(x) = (x2 - 9) / (x2 - 2x - 7)

D. f(x) = (x2 + x - 30) / (x2 + 5x - 14)

 May 19, 2019
 #1
avatar+6193 
+1

you need to factor the numerator and denominator of each choice and look for the one that

has a common term in both.

 

\(A.~\dfrac{x^2+5x+4}{x^2+x-12} = \dfrac{(x+4)(x+1)}{(x+4)(x-3)}\\ \text{and thus choice A has a hole at $x=-4$}\)

 

There may be other choices that have a hole as well.  I didn't check.

.
 May 19, 2019
edited by Rom  May 19, 2019
edited by Rom  May 19, 2019

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