Algebra Examples

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

Step 1

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

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Step 1.1

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 $- 1$ .

$- 2, 1$

Step 1.2

Write the factored form using these integers.

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

Step 2

Cancel the common factors.

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Step 2.1

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

$\frac{x + 1}{x - 2}$

Step 3

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

No holes

Step 4