Basic Math Examples

$q - \frac{1}{q} \div q + \frac{1}{q}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$q + \frac{- \frac{1}{q} + 1}{q}$

Step 1.2

Write $1$ as a fraction with a common denominator.

$q + \frac{- \frac{1}{q} + \frac{q}{q}}{q}$

Step 1.3

Combine the numerators over the common denominator.

$q + \frac{\frac{- 1 + q}{q}}{q}$

Step 1.4

Rewrite $- 1$ as $- 1 (1)$ .

$q + \frac{\frac{- 1 (1) + q}{q}}{q}$

Step 1.5

Factor $- 1$ out of $q$ .

$q + \frac{\frac{- 1 (1) - 1 (- q)}{q}}{q}$

Step 1.6

Factor $- 1$ out of $- 1 (1) - 1 (- q)$ .

$q + \frac{\frac{- 1 (1 - q)}{q}}{q}$

Step 1.7

Move the negative in front of the fraction.

$q + \frac{- \frac{1 - q}{q}}{q}$

Step 2

Simplify each term.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$q - \frac{1 - q}{q} \cdot \frac{1}{q}$

Step 2.2

Multiply $- \frac{1 - q}{q} \cdot \frac{1}{q}$ .

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Step 2.2.1

Multiply $\frac{1}{q}$ by $\frac{1 - q}{q}$ .

$q - \frac{1 - q}{q \cdot q}$

Step 2.2.2

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

$q - \frac{1 - q}{q^{1} q}$

Step 2.2.3

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

$q - \frac{1 - q}{q^{1} q^{1}}$

Step 2.2.4

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

$q - \frac{1 - q}{q^{1 + 1}}$

Step 2.2.5

Add $1$ and $1$ .

$q - \frac{1 - q}{q^{2}}$

Step 3

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

$\frac{q \cdot q^{2}}{q^{2}} - \frac{1 - q}{q^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{q \cdot q^{2} - (1 - q)}{q^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

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

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Step 5.1.1

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

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Step 5.1.1.1

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

$\frac{q^{1} q^{2} - (1 - q)}{q^{2}}$

Step 5.1.1.2

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

$\frac{q^{1 + 2} - (1 - q)}{q^{2}}$

Step 5.1.2

Add $1$ and $2$ .

$\frac{q^{3} - (1 - q)}{q^{2}}$

Step 5.2

Apply the distributive property.

$\frac{q^{3} - 1 \cdot 1 - - q}{q^{2}}$

Step 5.3

Multiply $- 1$ by $1$ .

$\frac{q^{3} - 1 - - q}{q^{2}}$

Step 5.4

Multiply $- - q$ .

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Step 5.4.1

Multiply $- 1$ by $- 1$ .

$\frac{q^{3} - 1 + 1 q}{q^{2}}$

Step 5.4.2

Multiply $q$ by $1$ .

$\frac{q^{3} - 1 + q}{q^{2}}$

Step 5.5

Reorder terms.

$\frac{q^{3} + q - 1}{q^{2}}$