Pre-Algebra Examples

$\frac{x^{2} - 5 x + 6}{5} \cdot \frac{15}{x - 3}$

Step 1

Factor $x^{2} - 5 x + 6$ using the AC method.

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Step 1.1

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 $6$ and whose sum is $- 5$ .

$- 3, - 2$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 3) (x - 2)}{5} \cdot \frac{15}{x - 3}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x - 3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{(x - 3) (x - 2)}{5} \cdot \frac{15}{x - 3}$

Step 2.1.2

Rewrite the expression.

$\frac{x - 2}{5} \cdot 15$

Step 2.2

Cancel the common factor of $5$ .

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Step 2.2.1

Factor $5$ out of $15$ .

$\frac{x - 2}{5} \cdot (5 (3))$

Step 2.2.2

Cancel the common factor.

$\frac{x - 2}{5} \cdot (5 \cdot 3)$

Step 2.2.3

Rewrite the expression.

$(x - 2) \cdot 3$

Step 2.3

Apply the distributive property.

$x \cdot 3 - 2 \cdot 3$

Step 2.4

Simplify the expression.

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Step 2.4.1

Move $3$ to the left of $x$ .

$3 \cdot x - 2 \cdot 3$

Step 2.4.2

Multiply $- 2$ by $3$ .

$3 x - 6$