Simplify (r^2+3r+2)/(r+2)*(r-9)/(r+1)

$\frac{r^{2} + 3 r + 2}{r + 2} \cdot \frac{r - 9}{r + 1}$

Step 1

Factor $r^{2} + 3 r + 2$ 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 $3$ .

$1, 2$

Write the factored form using these integers.

$\frac{(r + 1) (r + 2)}{r + 2} \cdot \frac{r - 9}{r + 1}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $r + 1$ .

Cancel the common factor.

$\frac{(r + 1) (r + 2)}{r + 2} \cdot \frac{r - 9}{r + 1}$

Rewrite the expression.

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

Cancel the common factor of $r + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$1 \cdot (r - 9)$

Multiply $r - 9$ by $1$ .

$r - 9$

Simplify (r^2+3r+2)/(r+2)*(r-9)/(r+1)

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