Simplify ((m-6)/(m-2))÷((m-5)/(m^2+m-6))

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Factor $m^{2} + m - 6$ 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 $- 6$ and whose sum is $1$ .

$- 2, 3$

Write the factored form using these integers.

$\frac{m - 6}{m - 2} \cdot \frac{(m - 2) (m + 3)}{m - 5}$

Step 3

Simplify terms.

Cancel the common factor of $m - 2$ .

Cancel the common factor.

$\frac{m - 6}{m - 2} \cdot \frac{(m - 2) (m + 3)}{m - 5}$

Rewrite the expression.

$(m - 6) \frac{m + 3}{m - 5}$

Multiply $m - 6$ by $\frac{m + 3}{m - 5}$ .

$\frac{(m - 6) (m + 3)}{m - 5}$

Simplify ((m-6)/(m-2))÷((m-5)/(m^2+m-6))

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