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

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

Factor $x^{2} - x - 2$ 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 $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Write the factored form using these integers.

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

Cancel the common factors.

Factor $x - 2$ out of ${(x - 2)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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-x-2)/((x-2)^2)

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