Find the Holes in the Graph f(x)=(x^2+7x-18)/(2x^2+2x)

$f (x) = \frac{x^{2} + 7 x - 18}{2 x^{2} + 2 x}$

Factor $x^{2} + 7 x - 18$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $7$ .

$- 2, 9$

Write the factored form using these integers.

$f (x) = \frac{(x - 2) (x + 9)}{2 x^{2} + 2 x}$

Factor $2 x$ out of $2 x^{2} + 2 x$ .

Factor $2 x$ out of $2 x^{2}$ .

$f (x) = \frac{(x - 2) (x + 9)}{2 x (x) + 2 x}$

Factor $2 x$ out of $2 x$ .

$f (x) = \frac{(x - 2) (x + 9)}{2 x (x) + 2 x (1)}$

Factor $2 x$ out of $2 x (x) + 2 x (1)$ .

$f (x) = \frac{(x - 2) (x + 9)}{2 x (x + 1)}$

Since no factors can be removed from the denominator, there are no holes in the graph.

No holes

Find the Holes in the Graph f(x)=(x^2+7x-18)/(2x^2+2x)

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