Pre-Algebra Examples

$\frac{x^{2} - 9 x + 14}{x} \cdot \frac{x^{2}}{x - 7}$

Step 1

Factor $x^{2} - 9 x + 14$ 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 $14$ and whose sum is $- 9$ .

$- 7, - 2$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 7) (x - 2)}{x} \cdot \frac{x^{2}}{x - 7}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x - 7$ .

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Step 2.1.1

Cancel the common factor.

$\frac{(x - 7) (x - 2)}{x} \cdot \frac{x^{2}}{x - 7}$

Step 2.1.2

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $x$ .

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$(x - 2) \cdot x$

Step 2.3

Apply the distributive property.

$x \cdot x - 2 x$

Step 2.4

Multiply $x$ by $x$ .

$x^{2} - 2 x$