Simplify (m^2-6m+8)/(2m-2)*10/(m-4)

$\frac{m^{2} - 6 m + 8}{2 m - 2} \cdot \frac{10}{m - 4}$

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 $- 6$ .

$- 4, - 2$

Write the factored form using these integers.

$\frac{(m - 4) (m - 2)}{2 m - 2} \cdot \frac{10}{m - 4}$

Simplify terms.

Factor $2$ out of $2 m - 2$ .

Factor $2$ out of $2 m$ .

$\frac{(m - 4) (m - 2)}{2 (m) - 2} \cdot \frac{10}{m - 4}$

Factor $2$ out of $- 2$ .

$\frac{(m - 4) (m - 2)}{2 (m) + 2 (- 1)} \cdot \frac{10}{m - 4}$

Factor $2$ out of $2 (m) + 2 (- 1)$ .

$\frac{(m - 4) (m - 2)}{2 (m - 1)} \cdot \frac{10}{m - 4}$

Cancel the common factor of $m - 4$ .

Cancel the common factor.

$\frac{(m - 4) (m - 2)}{2 (m - 1)} \cdot \frac{10}{m - 4}$

Rewrite the expression.

$\frac{m - 2}{2 (m - 1)} \cdot 10$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{m - 2}{m - 1} \cdot 5$

Combine $\frac{m - 2}{m - 1}$ and $5$ .

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

Move $5$ to the left of $m - 2$ .

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

Simplify (m^2-6m+8)/(2m-2)*10/(m-4)

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