Algebra Examples

$\frac{9 m + 63}{m^{2} + 11 m + 28} \div \frac{9}{8 m + 32}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{9 m + 63}{m^{2} + 11 m + 28} \cdot \frac{8 m + 32}{9}$

Step 2

Factor $9$ out of $9 m + 63$ .

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Step 2.1

Factor $9$ out of $9 m$ .

$\frac{9 (m) + 63}{m^{2} + 11 m + 28} \cdot \frac{8 m + 32}{9}$

Step 2.2

Factor $9$ out of $63$ .

$\frac{9 m + 9 \cdot 7}{m^{2} + 11 m + 28} \cdot \frac{8 m + 32}{9}$

Step 2.3

Factor $9$ out of $9 m + 9 \cdot 7$ .

$\frac{9 (m + 7)}{m^{2} + 11 m + 28} \cdot \frac{8 m + 32}{9}$

Step 3

Factor $m^{2} + 11 m + 28$ using the AC method.

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Step 3.1

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 $28$ and whose sum is $11$ .

$4, 7$

Step 3.2

Write the factored form using these integers.

$\frac{9 (m + 7)}{(m + 4) (m + 7)} \cdot \frac{8 m + 32}{9}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $9$ .

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Step 4.1.1

Cancel the common factor.

$\frac{9 (m + 7)}{(m + 4) (m + 7)} \cdot \frac{8 m + 32}{9}$

Step 4.1.2

Rewrite the expression.

$\frac{m + 7}{(m + 4) (m + 7)} (8 m + 32)$

Step 4.2

Cancel the common factor of $m + 7$ .

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Step 4.2.1

Cancel the common factor.

$\frac{m + 7}{(m + 4) (m + 7)} (8 m + 32)$

Step 4.2.2

Rewrite the expression.

$\frac{1}{m + 4} (8 m + 32)$

Step 4.3

Multiply $\frac{1}{m + 4}$ by $8 m + 32$ .

$\frac{8 m + 32}{m + 4}$

Step 4.4

Factor $8$ out of $8 m + 32$ .

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Step 4.4.1

Factor $8$ out of $8 m$ .

$\frac{8 (m) + 32}{m + 4}$

Step 4.4.2

Factor $8$ out of $32$ .

$\frac{8 m + 8 \cdot 4}{m + 4}$

Step 4.4.3

Factor $8$ out of $8 m + 8 \cdot 4$ .

$\frac{8 (m + 4)}{m + 4}$

Step 4.5

Cancel the common factor of $m + 4$ .

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Step 4.5.1

Cancel the common factor.

$\frac{8 (m + 4)}{m + 4}$

Step 4.5.2

Divide $8$ by $1$ .

$8$