Cancel the Common Factors (6x-18)/(x^2-5x+6)

$\frac{6 x - 18}{x^{2} - 5 x + 6}$

Step 1

Factor $6$ out of $6 x - 18$ .

Factor $6$ out of $6 x$ .

$\frac{6 (x) - 18}{x^{2} - 5 x + 6}$

Factor $6$ out of $- 18$ .

$\frac{6 x + 6 \cdot - 3}{x^{2} - 5 x + 6}$

Factor $6$ out of $6 x + 6 \cdot - 3$ .

$\frac{6 (x - 3)}{x^{2} - 5 x + 6}$

Step 2

Factor $x^{2} - 5 x + 6$ 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 $- 5$ .

$- 3, - 2$

Write the factored form using these integers.

$\frac{6 (x - 3)}{(x - 3) (x - 2)}$

Step 3

Reduce the expression $\frac{6 (x - 3)}{(x - 3) (x - 2)}$ by cancelling the common factors.

Cancel the common factor.

$\frac{6 (x - 3)}{(x - 3) (x - 2)}$

Rewrite the expression.

$\frac{6}{x - 2}$

Cancel the Common Factors (6x-18)/(x^2-5x+6)

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