Simplify ((m^2+m-30)/(m^2+13m+42))÷((m-2)/(m+7))

$\frac{m^{2} + m - 30}{m^{2} + 13 m + 42} \div \frac{m - 2}{m + 7}$

To divide by a fraction, multiply by its reciprocal.

$\frac{m^{2} + m - 30}{m^{2} + 13 m + 42} \cdot \frac{m + 7}{m - 2}$

Factor $m^{2} + m - 30$ 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 $- 30$ and whose sum is $1$ .

$- 5, 6$

Write the factored form using these integers.

$\frac{(m - 5) (m + 6)}{m^{2} + 13 m + 42} \cdot \frac{m + 7}{m - 2}$

Factor $m^{2} + 13 m + 42$ 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 $42$ and whose sum is $13$ .

$6, 7$

Write the factored form using these integers.

$\frac{(m - 5) (m + 6)}{(m + 6) (m + 7)} \cdot \frac{m + 7}{m - 2}$

Simplify terms.

Cancel the common factor of $m + 7$ .

Factor $m + 7$ out of $(m + 6) (m + 7)$ .

$\frac{(m - 5) (m + 6)}{(m + 7) (m + 6)} \cdot \frac{m + 7}{m - 2}$

Cancel the common factor.

$\frac{(m - 5) (m + 6)}{(m + 7) (m + 6)} \cdot \frac{m + 7}{m - 2}$

Rewrite the expression.

$\frac{(m - 5) (m + 6)}{m + 6} \cdot \frac{1}{m - 2}$

Multiply $\frac{(m - 5) (m + 6)}{m + 6}$ by $\frac{1}{m - 2}$ .

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

Cancel the common factor of $m + 6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{m - 5}{m - 2}$

Simplify ((m^2+m-30)/(m^2+13m+42))÷((m-2)/(m+7))

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