Pre-Algebra Examples

$\frac{x^{2} - 25}{3 x} \div \frac{x + 5}{15 x^{5}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 25}{3 x} \cdot \frac{15 x^{5}}{x + 5}$

Step 2

Cancel the common factor of $3 x$ .

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Step 2.1

Factor $3 x$ out of $15 x^{5}$ .

$\frac{x^{2} - 25}{3 x} \cdot \frac{3 x (5 x^{4})}{x + 5}$

Step 2.2

Cancel the common factor.

$\frac{x^{2} - 25}{3 x} \cdot \frac{3 x (5 x^{4})}{x + 5}$

Step 2.3

Rewrite the expression.

$(x^{2} - 25) \frac{5 x^{4}}{x + 5}$

Step 3

Multiply $x^{2} - 25$ by $\frac{5 x^{4}}{x + 5}$ .

$\frac{(x^{2} - 25) (5 x^{4})}{x + 5}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $25$ as $5^{2}$ .

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

Step 4.2

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 $b = 5$ .

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

Step 5

Cancel the common factor of $x + 5$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $(x - 5) \cdot 5 x^{4}$ by $1$ .

$(x - 5) \cdot 5 x^{4}$

Step 6

Apply the distributive property.

$(x \cdot 5 - 5 \cdot 5) x^{4}$

Step 7

Move $5$ to the left of $x$ .

$(5 \cdot x - 5 \cdot 5) x^{4}$

Step 8

Multiply $- 5$ by $5$ .

$(5 \cdot x - 25) x^{4}$

Step 9

Apply the distributive property.

$5 x \cdot x^{4} - 25 x^{4}$

Step 10

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 10.1

Move $x^{4}$ .

$5 (x^{4} x) - 25 x^{4}$

Step 10.2

Multiply $x^{4}$ by $x$ .

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Step 10.2.1

Raise $x$ to the power of $1$ .

$5 (x^{4} x^{1}) - 25 x^{4}$

Step 10.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{4 + 1} - 25 x^{4}$

Step 10.3

Add $4$ and $1$ .

$5 x^{5} - 25 x^{4}$