Cancel the Common Factors (5x+10)/(x^2-x-6)

$\frac{5 x + 10}{x^{2} - x - 6}$

Step 1

Factor $5$ out of $5 x + 10$ .

Factor $5$ out of $5 x$ .

$\frac{5 (x) + 10}{x^{2} - x - 6}$

Factor $5$ out of $10$ .

$\frac{5 x + 5 \cdot 2}{x^{2} - x - 6}$

Factor $5$ out of $5 x + 5 \cdot 2$ .

$\frac{5 (x + 2)}{x^{2} - x - 6}$

Step 2

Factor $x^{2} - x - 6$ 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 $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

$\frac{5 (x + 2)}{(x - 3) (x + 2)}$

Step 3

Reduce the expression $\frac{5 (x + 2)}{(x - 3) (x + 2)}$ by cancelling the common factors.

Cancel the common factor.

$\frac{5 (x + 2)}{(x - 3) (x + 2)}$

Rewrite the expression.

$\frac{5}{x - 3}$

Cancel the Common Factors (5x+10)/(x^2-x-6)

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