Pre-Algebra Examples

$\frac{x^{2}}{x - 7} - \frac{14 x - 49}{x - 7}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{x^{2} - (14 x - 49)}{x - 7}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{x^{2} - (14 x) - - 49}{x - 7}$

Step 1.2.2

Multiply $14$ by $- 1$ .

$\frac{x^{2} - 14 x - - 49}{x - 7}$

Step 1.2.3

Multiply $- 1$ by $- 49$ .

$\frac{x^{2} - 14 x + 49}{x - 7}$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $49$ as $7^{2}$ .

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

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$14 x = 2 \cdot x \cdot 7$

Step 2.3

Rewrite the polynomial.

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

Step 2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7$ .

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

Step 3

Cancel the common factor of ${(x - 7)}^{2}$ and $x - 7$ .

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Step 3.1

Factor $x - 7$ out of ${(x - 7)}^{2}$ .

$\frac{(x - 7) (x - 7)}{x - 7}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{(x - 7) (x - 7)}{(x - 7) \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{(x - 7) (x - 7)}{(x - 7) \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{x - 7}{1}$

Step 3.2.4

Divide $x - 7$ by $1$ .

$x - 7$