Finite Math Examples

$\frac{25 x^{4} - 225}{5 x^{2} + 15}$

Step 1

Cancel the common factor of $25 x^{4} - 225$ and $5 x^{2} + 15$ .

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Step 1.1

Factor $5$ out of $25 x^{4}$ .

$\frac{5 (5 x^{4}) - 225}{5 x^{2} + 15}$

Step 1.2

Factor $5$ out of $- 225$ .

$\frac{5 (5 x^{4}) + 5 \cdot - 45}{5 x^{2} + 15}$

Step 1.3

Factor $5$ out of $5 (5 x^{4}) + 5 (- 45)$ .

$\frac{5 (5 x^{4} - 45)}{5 x^{2} + 15}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $5$ out of $5 x^{2}$ .

$\frac{5 (5 x^{4} - 45)}{5 (x^{2}) + 15}$

Step 1.4.2

Factor $5$ out of $15$ .

$\frac{5 (5 x^{4} - 45)}{5 x^{2} + 5 \cdot 3}$

Step 1.4.3

Factor $5$ out of $5 x^{2} + 5 \cdot 3$ .

$\frac{5 (5 x^{4} - 45)}{5 (x^{2} + 3)}$

Step 1.4.4

Cancel the common factor.

$\frac{5 (5 x^{4} - 45)}{5 (x^{2} + 3)}$

Step 1.4.5

Rewrite the expression.

$\frac{5 x^{4} - 45}{x^{2} + 3}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $5$ out of $5 x^{4} - 45$ .

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Step 2.1.1

Factor $5$ out of $5 x^{4}$ .

$\frac{5 (x^{4}) - 45}{x^{2} + 3}$

Step 2.1.2

Factor $5$ out of $- 45$ .

$\frac{5 x^{4} + 5 \cdot - 9}{x^{2} + 3}$

Step 2.1.3

Factor $5$ out of $5 x^{4} + 5 \cdot - 9$ .

$\frac{5 (x^{4} - 9)}{x^{2} + 3}$

Step 2.2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\frac{5 ({(x^{2})}^{2} - 9)}{x^{2} + 3}$

Step 2.3

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

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

Step 2.4

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

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x^{2} + 3$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Divide $5 (x^{2} - 3)$ by $1$ .

$5 (x^{2} - 3)$

Step 3.2

Apply the distributive property.

$5 x^{2} + 5 \cdot - 3$

Step 3.3

Multiply $5$ by $- 3$ .

$5 x^{2} - 15$