Algebra Examples

$\frac{\frac{9}{4 x^{2}}}{\frac{6 x}{16 x^{4}}}$

Step 1

Cancel the common factor of $6$ and $16$ .

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Step 1.1

Factor $2$ out of $6 x$ .

$\frac{\frac{9}{4 x^{2}}}{\frac{2 (3 x)}{16 x^{4}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $16 x^{4}$ .

$\frac{\frac{9}{4 x^{2}}}{\frac{2 (3 x)}{2 (8 x^{4})}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{9}{4 x^{2}}}{\frac{2 (3 x)}{2 (8 x^{4})}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{9}{4 x^{2}}}{\frac{3 x}{8 x^{4}}}$

Step 2

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

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Step 2.1

Factor $x$ out of $3 x$ .

$\frac{\frac{9}{4 x^{2}}}{\frac{x \cdot 3}{8 x^{4}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x$ out of $8 x^{4}$ .

$\frac{\frac{9}{4 x^{2}}}{\frac{x \cdot 3}{x (8 x^{3})}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{9}{4 x^{2}}}{\frac{x \cdot 3}{x (8 x^{3})}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{9}{4 x^{2}}}{\frac{3}{8 x^{3}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{4 x^{2}} \cdot \frac{8 x^{3}}{3}$

Step 4

Combine.

$\frac{9 (8 x^{3})}{4 x^{2} \cdot 3}$

Step 5

Cancel the common factor of $9$ and $3$ .

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Step 5.1

Factor $3$ out of $9 (8 x^{3})$ .

$\frac{3 (3 (8 x^{3}))}{4 x^{2} \cdot 3}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $4 x^{2} \cdot 3$ .

$\frac{3 (3 (8 x^{3}))}{3 \cdot (4 x^{2})}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (3 (8 x^{3}))}{3 \cdot (4 x^{2})}$

Step 5.2.3

Rewrite the expression.

$\frac{3 (8 x^{3})}{4 x^{2}}$

Step 6

Cancel the common factor of $8$ and $4$ .

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Step 6.1

Factor $4$ out of $3 (8 x^{3})$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Multiply by $1$ .

$\frac{x^{2} (3 (2 x))}{x^{2} \cdot 1}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{2} (3 (2 x))}{x^{2} \cdot 1}$

Step 7.2.3

Rewrite the expression.

$\frac{3 (2 x)}{1}$

Step 7.2.4

Divide $3 (2 x)$ by $1$ .

$3 (2 x)$

Step 8

Multiply $2$ by $3$ .

$6 x$