Question

Given the function f ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20 Describe where the function has a hole and how you found your answer.

Answer 1

${x}^{2} + 7x + \frac{10}{ {x}^{2} } + 9x + 20 \\ = {x}^{2} + 16x + \frac{10}{ {x}^{2} } + 20 \\ x = 0 \\ \frac{10}{ {x}^{2} } = \frac{10}{0}$

= undefined

It is undefined as you cannot divide by zero. Hence, there is a hole at x = 0.