Simplify (x^2-x-6)/(x-3)*(x+9)/(x+2)

$\frac{x^{2} - x - 6}{x - 3} \cdot \frac{x + 9}{x + 2}$

Step 1

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.

$\frac{(x - 3) (x + 2)}{x - 3} \cdot \frac{x + 9}{x + 2}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $(x - 3) (x + 2)$ .

$\frac{(x + 2) (x - 3)}{x - 3} \cdot \frac{x + 9}{x + 2}$

Cancel the common factor.

$\frac{(x + 2) (x - 3)}{x - 3} \cdot \frac{x + 9}{x + 2}$

Rewrite the expression.

$\frac{x - 3}{x - 3} \cdot (x + 9)$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{x - 3}{x - 3} \cdot (x + 9)$

Rewrite the expression.

$1 \cdot (x + 9)$

Multiply $x + 9$ by $1$ .

$x + 9$

Simplify (x^2-x-6)/(x-3)*(x+9)/(x+2)

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