Basic Math Examples

$v + \frac{6}{v} \div v + \frac{v}{6}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$v + \frac{\frac{6}{v}}{v} + \frac{v}{6}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$v + \frac{6}{v} \cdot \frac{1}{v} + \frac{v}{6}$

Step 1.3

Multiply $\frac{6}{v} \cdot \frac{1}{v}$ .

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Step 1.3.1

Multiply $\frac{6}{v}$ by $\frac{1}{v}$ .

$v + \frac{6}{v \cdot v} + \frac{v}{6}$

Step 1.3.2

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

$v + \frac{6}{v^{1} v} + \frac{v}{6}$

Step 1.3.3

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

$v + \frac{6}{v^{1} v^{1}} + \frac{v}{6}$

Step 1.3.4

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

$v + \frac{6}{v^{1 + 1}} + \frac{v}{6}$

Step 1.3.5

Add $1$ and $1$ .

$v + \frac{6}{v^{2}} + \frac{v}{6}$

Step 2

To write $v$ as a fraction with a common denominator, multiply by $\frac{v^{2}}{v^{2}}$ .

$\frac{v \cdot v^{2}}{v^{2}} + \frac{6}{v^{2}} + \frac{v}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{v \cdot v^{2} + 6}{v^{2}} + \frac{v}{6}$

Step 4

Multiply $v$ by $v^{2}$ by adding the exponents.

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Step 4.1

Multiply $v$ by $v^{2}$ .

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Step 4.1.1

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

$\frac{v^{1} v^{2} + 6}{v^{2}} + \frac{v}{6}$

Step 4.1.2

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

$\frac{v^{1 + 2} + 6}{v^{2}} + \frac{v}{6}$

Step 4.2

Add $1$ and $2$ .

$\frac{v^{3} + 6}{v^{2}} + \frac{v}{6}$

Step 5

To write $\frac{v^{3} + 6}{v^{2}}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{v^{3} + 6}{v^{2}} \cdot \frac{6}{6} + \frac{v}{6}$

Step 6

To write $\frac{v}{6}$ as a fraction with a common denominator, multiply by $\frac{v^{2}}{v^{2}}$ .

$\frac{v^{3} + 6}{v^{2}} \cdot \frac{6}{6} + \frac{v}{6} \cdot \frac{v^{2}}{v^{2}}$

Step 7

Write each expression with a common denominator of $6 v^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{v^{3} + 6}{v^{2}}$ by $\frac{6}{6}$ .

$\frac{(v^{3} + 6) \cdot 6}{v^{2} \cdot 6} + \frac{v}{6} \cdot \frac{v^{2}}{v^{2}}$

Step 7.2

Multiply $\frac{v}{6}$ by $\frac{v^{2}}{v^{2}}$ .

$\frac{(v^{3} + 6) \cdot 6}{v^{2} \cdot 6} + \frac{v \cdot v^{2}}{6 v^{2}}$

Step 7.3

Reorder the factors of $v^{2} \cdot 6$ .

$\frac{(v^{3} + 6) \cdot 6}{6 v^{2}} + \frac{v \cdot v^{2}}{6 v^{2}}$

Step 8

Combine the numerators over the common denominator.

$\frac{(v^{3} + 6) \cdot 6 + v \cdot v^{2}}{6 v^{2}}$

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

$\frac{v^{3} \cdot 6 + 6 \cdot 6 + v \cdot v^{2}}{6 v^{2}}$

Step 9.2

Move $6$ to the left of $v^{3}$ .

$\frac{6 \cdot v^{3} + 6 \cdot 6 + v \cdot v^{2}}{6 v^{2}}$

Step 9.3

Multiply $6$ by $6$ .

$\frac{6 \cdot v^{3} + 36 + v \cdot v^{2}}{6 v^{2}}$

Step 9.4

Multiply $v$ by $v^{2}$ by adding the exponents.

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Step 9.4.1

Multiply $v$ by $v^{2}$ .

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Step 9.4.1.1

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

$\frac{6 v^{3} + 36 + v^{1} v^{2}}{6 v^{2}}$

Step 9.4.1.2

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

$\frac{6 v^{3} + 36 + v^{1 + 2}}{6 v^{2}}$

Step 9.4.2

Add $1$ and $2$ .

$\frac{6 v^{3} + 36 + v^{3}}{6 v^{2}}$

Step 9.5

Add $6 v^{3}$ and $v^{3}$ .

$\frac{7 v^{3} + 36}{6 v^{2}}$