Divide ((10m-90)/10)÷((m^2+9m+18)/(7m^2+42m))

$\frac{10 m - 90}{10} \div \frac{m^{2} + 9 m + 18}{7 m^{2} + 42 m}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 m - 90}{10} \cdot \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Step 2

Cancel the common factor of $10 m - 90$ and $10$ .

Factor $10$ out of $10 m$ .

$\frac{10 (m) - 90}{10} \cdot \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Factor $10$ out of $- 90$ .

$\frac{10 (m) + 10 \cdot - 9}{10} \cdot \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Factor $10$ out of $10 (m) + 10 (- 9)$ .

$\frac{10 (m - 9)}{10} \cdot \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Cancel the common factors.

Factor $10$ out of $10$ .

$\frac{10 (m - 9)}{10 (1)} \cdot \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Cancel the common factor.

$\frac{10 (m - 9)}{10 \cdot 1} \cdot \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Rewrite the expression.

$\frac{m - 9}{1} \cdot \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Divide $m - 9$ by $1$ .

$(m - 9) \frac{7 m^{2} + 42 m}{m^{2} + 9 m + 18}$

Step 3

Factor $7 m$ out of $7 m^{2} + 42 m$ .

Factor $7 m$ out of $7 m^{2}$ .

$(m - 9) \frac{7 m (m) + 42 m}{m^{2} + 9 m + 18}$

Factor $7 m$ out of $42 m$ .

$(m - 9) \frac{7 m (m) + 7 m (6)}{m^{2} + 9 m + 18}$

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

$(m - 9) \frac{7 m (m + 6)}{m^{2} + 9 m + 18}$

Step 4

Factor $m^{2} + 9 m + 18$ 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 $18$ and whose sum is $9$ .

$3, 6$

Write the factored form using these integers.

$(m - 9) \frac{7 m (m + 6)}{(m + 3) (m + 6)}$

Step 5

Cancel the common factor of $m + 6$ .

Cancel the common factor.

$(m - 9) \frac{7 m (m + 6)}{(m + 3) (m + 6)}$

Rewrite the expression.

$(m - 9) \frac{7 m}{m + 3}$

Step 6

Multiply $m - 9$ by $\frac{7 m}{m + 3}$ .

$\frac{(m - 9) (7 m)}{m + 3}$

Step 7

Move $7$ to the left of $m - 9$ .

$\frac{7 \cdot (m - 9) m}{m + 3}$

Step 8

Reorder factors in $\frac{7 (m - 9) m}{m + 3}$ .

$\frac{7 m (m - 9)}{m + 3}$

Divide ((10m-90)/10)÷((m^2+9m+18)/(7m^2+42m))

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