Finite Math Examples

$\frac{\frac{x^{3}}{5 x^{15}}}{\frac{5 x}{25 x^{4}}}$

Step 1

Cancel the common factor of $x^{3}$ and $x^{15}$ .

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Step 1.1

Multiply by $1$ .

$\frac{\frac{x^{3} \cdot 1}{5 x^{15}}}{\frac{5 x}{25 x^{4}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

$\frac{\frac{x^{3} \cdot 1}{x^{3} (5 x^{12})}}{\frac{5 x}{25 x^{4}}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{x^{3} \cdot 1}{x^{3} (5 x^{12})}}{\frac{5 x}{25 x^{4}}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{1}{5 x^{12}}}{\frac{5 x}{25 x^{4}}}$

Step 2

Cancel the common factor of $5$ and $25$ .

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Step 2.1

Factor $5$ out of $5 x$ .

$\frac{\frac{1}{5 x^{12}}}{\frac{5 (x)}{25 x^{4}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{\frac{1}{5 x^{12}}}{\frac{5 (x)}{5 (5 x^{4})}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{1}{5 x^{12}}}{\frac{5 x}{5 (5 x^{4})}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{1}{5 x^{12}}}{\frac{x}{5 x^{4}}}$

Step 3

Cancel the common factor of $x$ and $x^{4}$ .

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Step 3.1

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

$\frac{\frac{1}{5 x^{12}}}{\frac{x^{1}}{5 x^{4}}}$

Step 3.2

Factor $x$ out of $x^{1}$ .

$\frac{\frac{1}{5 x^{12}}}{\frac{x \cdot 1}{5 x^{4}}}$

Step 3.3

Cancel the common factors.

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Step 3.3.1

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

$\frac{\frac{1}{5 x^{12}}}{\frac{x \cdot 1}{x (5 x^{3})}}$

Step 3.3.2

Cancel the common factor.

$\frac{\frac{1}{5 x^{12}}}{\frac{x \cdot 1}{x (5 x^{3})}}$

Step 3.3.3

Rewrite the expression.

$\frac{\frac{1}{5 x^{12}}}{\frac{1}{5 x^{3}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{5 x^{12}} (5 x^{3})$

Step 5

Rewrite using the commutative property of multiplication.

$5 \frac{1}{5 x^{12}} x^{3}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $5 x^{12}$ .

$5 \frac{1}{5 (x^{12})} x^{3}$

Step 6.2

Cancel the common factor.

$5 \frac{1}{5 x^{12}} x^{3}$

Step 6.3

Rewrite the expression.

$\frac{1}{x^{12}} x^{3}$

Step 7

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

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Step 7.1

Factor $x^{3}$ out of $x^{12}$ .

$\frac{1}{x^{3} x^{9}} x^{3}$

Step 7.2

Cancel the common factor.

$\frac{1}{x^{3} x^{9}} x^{3}$

Step 7.3

Rewrite the expression.

$\frac{1}{x^{9}}$