Pre-Algebra Examples

$\frac{m + 6}{m - 4} \div \frac{m + 4}{m^{2} - 5 m + 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{m + 6}{m - 4} \cdot \frac{m^{2} - 5 m + 4}{m + 4}$

Step 2

Factor $m^{2} - 5 m + 4$ using the AC method.

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Step 2.1

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 $4$ and whose sum is $- 5$ .

$- 4, - 1$

Step 2.2

Write the factored form using these integers.

$\frac{m + 6}{m - 4} \cdot \frac{(m - 4) (m - 1)}{m + 4}$

Step 3

Cancel the common factor of $m - 4$ .

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Step 3.1

Cancel the common factor.

$\frac{m + 6}{m - 4} \cdot \frac{(m - 4) (m - 1)}{m + 4}$

Step 3.2

Rewrite the expression.

$(m + 6) \frac{m - 1}{m + 4}$

Step 4

Multiply $m + 6$ by $\frac{m - 1}{m + 4}$ .

$\frac{(m + 6) (m - 1)}{m + 4}$