Factor (x^2-5x+6)/(x^2-3x)

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

Step 1

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.

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

Step 2

Factor $x$ out of $x^{2} - 3 x$ .

Factor $x$ out of $x^{2}$ .

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

Factor $x$ out of $- 3 x$ .

$\frac{(x - 3) (x - 2)}{x \cdot x + x \cdot - 3}$

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

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

Step 3

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

Cancel the common factor.

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

Rewrite the expression.

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

Factor (x^2-5x+6)/(x^2-3x)

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