Algebra Examples

$\frac{5 x^{2} - 7 - 2 (2 x^{2} + 1)}{x - 3}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the distributive property.

$\frac{5 x^{2} - 7 - 2 (2 x^{2}) - 2 \cdot 1}{x - 3}$

Step 1.2

Multiply $2$ by $- 2$ .

$\frac{5 x^{2} - 7 - 4 x^{2} - 2 \cdot 1}{x - 3}$

Step 1.3

Multiply $- 2$ by $1$ .

$\frac{5 x^{2} - 7 - 4 x^{2} - 2}{x - 3}$

Step 1.4

Subtract $4 x^{2}$ from $5 x^{2}$ .

$\frac{x^{2} - 7 - 2}{x - 3}$

Step 1.5

Subtract $2$ from $- 7$ .

$\frac{x^{2} - 9}{x - 3}$

Step 1.6

Rewrite $x^{2} - 9$ in a factored form.

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Step 1.6.1

Rewrite $9$ as $3^{2}$ .

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

Step 1.6.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

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

Step 2

Cancel the common factor of $x - 3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $x + 3$ by $1$ .

$x + 3$