Basic Math Examples

$\frac{9 y^{2}}{y^{2 + 2 y + 1}} \div \frac{36 y}{y^{2 - 1}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{9 y^{2}}{y^{2 + 2 y + 1}} \cdot \frac{y^{2 - 1}}{36 y}$

Step 2

Combine.

$\frac{9 y^{2} y^{2 - 1}}{y^{2 + 2 y + 1} (36 y)}$

Step 3

Multiply $y^{2}$ by $y^{2 - 1}$ by adding the exponents.

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Step 3.1

Move $y^{2 - 1}$ .

$\frac{9 (y^{2 - 1} y^{2})}{y^{2 + 2 y + 1} (36 y)}$

Step 3.2

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

$\frac{9 y^{2 - 1 + 2}}{y^{2 + 2 y + 1} (36 y)}$

Step 3.3

Subtract $1$ from $2$ .

$\frac{9 y^{1 + 2}}{y^{2 + 2 y + 1} (36 y)}$

Step 3.4

Add $1$ and $2$ .

$\frac{9 y^{3}}{y^{2 + 2 y + 1} (36 y)}$

Step 4

Multiply $y^{2 + 2 y + 1}$ by $y$ by adding the exponents.

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Step 4.1

Move $y$ .

$\frac{9 y^{3}}{y \cdot y^{2 + 2 y + 1} \cdot 36}$

Step 4.2

Multiply $y$ by $y^{2 + 2 y + 1}$ .

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Step 4.2.1

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

$\frac{9 y^{3}}{y^{1} y^{2 + 2 y + 1} \cdot 36}$

Step 4.2.2

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

$\frac{9 y^{3}}{y^{1 + 2 + 2 y + 1} \cdot 36}$

Step 4.3

Add $2$ and $1$ .

$\frac{9 y^{3}}{y^{1 + 2 y + 3} \cdot 36}$

Step 4.4

Add $1$ and $3$ .

$\frac{9 y^{3}}{y^{2 y + 4} \cdot 36}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $9$ and $36$ .

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Step 5.1.1

Factor $9$ out of $9 y^{3}$ .

$\frac{9 (y^{3})}{y^{2 y + 4} \cdot 36}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $9$ out of $y^{2 y + 4} \cdot 36$ .

$\frac{9 (y^{3})}{9 (y^{2 y + 4} \cdot 4)}$

Step 5.1.2.2

Cancel the common factor.

$\frac{9 y^{3}}{9 (y^{2 y + 4} \cdot 4)}$

Step 5.1.2.3

Rewrite the expression.

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

Step 5.2

Cancel the common factor of $y^{3}$ and $y^{2 y + 4}$ .

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Step 5.2.1

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

$\frac{y^{2 y + 4} y^{3 - (2 y + 4)}}{y^{2 y + 4} \cdot 4}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $y^{2 y + 4}$ out of $y^{2 y + 4} \cdot 4$ .

$\frac{y^{2 y + 4} y^{3 - (2 y + 4)}}{y^{2 y + 4} (4)}$

Step 5.2.2.2

Cancel the common factor.

$\frac{y^{2 y + 4} y^{3 - (2 y + 4)}}{y^{2 y + 4} \cdot 4}$

Step 5.2.2.3

Rewrite the expression.

$\frac{y^{3 - (2 y + 4)}}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Simplify each term.

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Step 6.1.1

Apply the distributive property.

$\frac{y^{3 - (2 y) - 1 \cdot 4}}{4}$

Step 6.1.2

Multiply $2$ by $- 1$ .

$\frac{y^{3 - 2 y - 1 \cdot 4}}{4}$

Step 6.1.3

Multiply $- 1$ by $4$ .

$\frac{y^{3 - 2 y - 4}}{4}$

Step 6.2

Subtract $4$ from $3$ .

$\frac{y^{- 2 y - 1}}{4}$