Algebra Examples

$\frac{7 x^{2}}{12 x} \div \frac{14 x^{3}}{48 y^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 x^{2}}{12 x} \cdot \frac{48 y^{3}}{14 x^{3}}$

Step 2

Combine.

$\frac{7 x^{2} (48 y^{3})}{12 x (14 x^{3})}$

Step 3

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 3.1

Move $x^{3}$ .

$\frac{7 x^{2} (48 y^{3})}{12 (x^{3} x) \cdot 14}$

Step 3.2

Multiply $x^{3}$ by $x$ .

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Step 3.2.1

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

$\frac{7 x^{2} (48 y^{3})}{12 (x^{3} x^{1}) \cdot 14}$

Step 3.2.2

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

$\frac{7 x^{2} (48 y^{3})}{12 x^{3 + 1} \cdot 14}$

Step 3.3

Add $3$ and $1$ .

$\frac{7 x^{2} (48 y^{3})}{12 x^{4} \cdot 14}$

Step 4

Cancel the common factor of $7$ and $14$ .

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Step 4.1

Factor $7$ out of $7 x^{2} (48 y^{3})$ .

$\frac{7 (x^{2} (48 y^{3}))}{12 x^{4} \cdot 14}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $7$ out of $12 x^{4} \cdot 14$ .

$\frac{7 (x^{2} (48 y^{3}))}{7 (12 x^{4} \cdot 2)}$

Step 4.2.2

Cancel the common factor.

$\frac{7 (x^{2} (48 y^{3}))}{7 (12 x^{4} \cdot 2)}$

Step 4.2.3

Rewrite the expression.

$\frac{x^{2} (48 y^{3})}{12 x^{4} \cdot 2}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $x^{2}$ out of $12 x^{4} \cdot 2$ .

$\frac{x^{2} (48 y^{3})}{x^{2} (12 x^{2} \cdot 2)}$

Step 5.2

Cancel the common factor.

$\frac{x^{2} (48 y^{3})}{x^{2} (12 x^{2} \cdot 2)}$

Step 5.3

Rewrite the expression.

$\frac{48 y^{3}}{12 x^{2} \cdot 2}$

Step 6

Cancel the common factor of $48$ and $12$ .

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Step 6.1

Factor $12$ out of $48 y^{3}$ .

$\frac{12 (4 y^{3})}{12 x^{2} \cdot 2}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $12$ out of $12 x^{2} \cdot 2$ .

$\frac{12 (4 y^{3})}{12 (x^{2} \cdot 2)}$

Step 6.2.2

Cancel the common factor.

$\frac{12 (4 y^{3})}{12 (x^{2} \cdot 2)}$

Step 6.2.3

Rewrite the expression.

$\frac{4 y^{3}}{x^{2} \cdot 2}$

Step 7

Cancel the common factor of $4$ and $2$ .

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Step 7.1

Factor $2$ out of $4 y^{3}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{2 y^{3}}{x^{2}}$