Pre-Algebra Examples

$\frac{6 x^{2} - 54}{4 x^{2} - 36}$

Step 1

Cancel the common factor of $6 x^{2} - 54$ and $4 x^{2} - 36$ .

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Step 1.1

Factor $2$ out of $6 x^{2}$ .

$\frac{2 (3 x^{2}) - 54}{4 x^{2} - 36}$

Step 1.2

Factor $2$ out of $- 54$ .

$\frac{2 (3 x^{2}) + 2 (- 27)}{4 x^{2} - 36}$

Step 1.3

Factor $2$ out of $2 (3 x^{2}) + 2 (- 27)$ .

$\frac{2 (3 x^{2} - 27)}{4 x^{2} - 36}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $4 x^{2}$ .

$\frac{2 (3 x^{2} - 27)}{2 (2 x^{2}) - 36}$

Step 1.4.2

Factor $2$ out of $- 36$ .

$\frac{2 (3 x^{2} - 27)}{2 (2 x^{2}) + 2 (- 18)}$

Step 1.4.3

Factor $2$ out of $2 (2 x^{2}) + 2 (- 18)$ .

$\frac{2 (3 x^{2} - 27)}{2 (2 x^{2} - 18)}$

Step 1.4.4

Cancel the common factor.

$\frac{2 (3 x^{2} - 27)}{2 (2 x^{2} - 18)}$

Step 1.4.5

Rewrite the expression.

$\frac{3 x^{2} - 27}{2 x^{2} - 18}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $3$ out of $3 x^{2} - 27$ .

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Step 2.1.1

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

$\frac{3 (x^{2}) - 27}{2 x^{2} - 18}$

Step 2.1.2

Factor $3$ out of $- 27$ .

$\frac{3 x^{2} + 3 \cdot - 9}{2 x^{2} - 18}$

Step 2.1.3

Factor $3$ out of $3 x^{2} + 3 \cdot - 9$ .

$\frac{3 (x^{2} - 9)}{2 x^{2} - 18}$

Step 2.2

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

$\frac{3 (x^{2} - 3^{2})}{2 x^{2} - 18}$

Step 2.3

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 $b = 3$ .

$\frac{3 (x + 3) (x - 3)}{2 x^{2} - 18}$

Step 3

Simplify the denominator.

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Step 3.1

Factor $2$ out of $2 x^{2} - 18$ .

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Step 3.1.1

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

$\frac{3 (x + 3) (x - 3)}{2 (x^{2}) - 18}$

Step 3.1.2

Factor $2$ out of $- 18$ .

$\frac{3 (x + 3) (x - 3)}{2 x^{2} + 2 \cdot - 9}$

Step 3.1.3

Factor $2$ out of $2 x^{2} + 2 \cdot - 9$ .

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

Step 3.2

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

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

Step 3.3

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 $b = 3$ .

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $x + 3$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $x - 3$ .

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

$\frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$