Pre-Algebra Examples

$\frac{3 x^{2} - 48}{9 x - 36}$

Step 1

Cancel the common factor of $3 x^{2} - 48$ and $9 x - 36$ .

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Step 1.1

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

$\frac{3 (x^{2}) - 48}{9 x - 36}$

Step 1.2

Factor $3$ out of $- 48$ .

$\frac{3 x^{2} + 3 \cdot - 16}{9 x - 36}$

Step 1.3

Factor $3$ out of $3 x^{2} + 3 \cdot - 16$ .

$\frac{3 (x^{2} - 16)}{9 x - 36}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $9 x$ .

$\frac{3 (x^{2} - 16)}{3 (3 x) - 36}$

Step 1.4.2

Factor $3$ out of $- 36$ .

$\frac{3 (x^{2} - 16)}{3 (3 x) + 3 (- 12)}$

Step 1.4.3

Factor $3$ out of $3 (3 x) + 3 (- 12)$ .

$\frac{3 (x^{2} - 16)}{3 (3 x - 12)}$

Step 1.4.4

Cancel the common factor.

$\frac{3 (x^{2} - 16)}{3 (3 x - 12)}$

Step 1.4.5

Rewrite the expression.

$\frac{x^{2} - 16}{3 x - 12}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{x^{2} - 4^{2}}{3 x - 12}$

Step 2.2

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 $b = 4$ .

$\frac{(x + 4) (x - 4)}{3 x - 12}$

Step 3

Factor $3$ out of $3 x - 12$ .

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Step 3.1

Factor $3$ out of $3 x$ .

$\frac{(x + 4) (x - 4)}{3 (x) - 12}$

Step 3.2

Factor $3$ out of $- 12$ .

$\frac{(x + 4) (x - 4)}{3 x + 3 \cdot - 4}$

Step 3.3

Factor $3$ out of $3 x + 3 \cdot - 4$ .

$\frac{(x + 4) (x - 4)}{3 (x - 4)}$

Step 4

Cancel the common factor of $x - 4$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{3 (x - 4)}$

Step 4.2

Rewrite the expression.

$\frac{x + 4}{3}$

Step 5

Split the fraction $\frac{x + 4}{3}$ into two fractions.

$\frac{x}{3} + \frac{4}{3}$