Simplify (m^2+7m+12)/(m^2+6m+8)

$\frac{m^{2} + 7 m + 12}{m^{2} + 6 m + 8}$

Step 1

Factor $m^{2} + 7 m + 12$ 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 $12$ and whose sum is $7$ .

$3, 4$

Write the factored form using these integers.

$\frac{(m + 3) (m + 4)}{m^{2} + 6 m + 8}$

Step 2

Factor $m^{2} + 6 m + 8$ 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 $8$ and whose sum is $6$ .

$2, 4$

Write the factored form using these integers.

$\frac{(m + 3) (m + 4)}{(m + 2) (m + 4)}$

Step 3

Cancel the common factor of $m + 4$ .

Cancel the common factor.

$\frac{(m + 3) (m + 4)}{(m + 2) (m + 4)}$

Rewrite the expression.

$\frac{m + 3}{m + 2}$

Simplify (m^2+7m+12)/(m^2+6m+8)

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