Basic Math Examples

$(i q r) = q^{3} - q$

Step 1

Divide each term in $i q r = q^{3} - q$ by $i q$ .

$\frac{i q r}{i q} = \frac{q^{3}}{i q} + \frac{- q}{i q}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $i$ .

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Step 2.1.1

Cancel the common factor.

$\frac{i q r}{i q} = \frac{q^{3}}{i q} + \frac{- q}{i q}$

Step 2.1.2

Rewrite the expression.

$\frac{q r}{q} = \frac{q^{3}}{i q} + \frac{- q}{i q}$

Step 2.2

Cancel the common factor of $q$ .

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Step 2.2.1

Cancel the common factor.

$\frac{q r}{q} = \frac{q^{3}}{i q} + \frac{- q}{i q}$

Step 2.2.2

Divide $r$ by $1$ .

$r = \frac{q^{3}}{i q} + \frac{- q}{i q}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

Factor $q$ out of $q^{3}$ .

$r = \frac{q \cdot q^{2}}{i q} + \frac{- q}{i q}$

Step 3.1.1.2

Cancel the common factors.

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Step 3.1.1.2.1

Factor $q$ out of $i q$ .

$r = \frac{q \cdot q^{2}}{q i} + \frac{- q}{i q}$

Step 3.1.1.2.2

Cancel the common factor.

$r = \frac{q \cdot q^{2}}{q i} + \frac{- q}{i q}$

Step 3.1.1.2.3

Rewrite the expression.

$r = \frac{q^{2}}{i} + \frac{- q}{i q}$

Step 3.1.2

Multiply the numerator and denominator of $\frac{q^{2}}{i}$ by the conjugate of $i$ to make the denominator real.

$r = \frac{q^{2}}{i} \cdot \frac{i}{i} + \frac{- q}{i q}$

Step 3.1.3

Multiply.

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Step 3.1.3.1

Combine.

$r = \frac{q^{2} i}{i i} + \frac{- q}{i q}$

Step 3.1.3.2

Simplify the denominator.

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Step 3.1.3.2.1

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

$r = \frac{q^{2} i}{i^{1} i} + \frac{- q}{i q}$

Step 3.1.3.2.2

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

$r = \frac{q^{2} i}{i^{1} i^{1}} + \frac{- q}{i q}$

Step 3.1.3.2.3

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

$r = \frac{q^{2} i}{i^{1 + 1}} + \frac{- q}{i q}$

Step 3.1.3.2.4

Add $1$ and $1$ .

$r = \frac{q^{2} i}{i^{2}} + \frac{- q}{i q}$

Step 3.1.3.2.5

Rewrite $i^{2}$ as $- 1$ .

$r = \frac{q^{2} i}{- 1} + \frac{- q}{i q}$

Step 3.1.4

Move the negative one from the denominator of $\frac{q^{2} i}{- 1}$ .

$r = - 1 \cdot (q^{2} i) + \frac{- q}{i q}$

Step 3.1.5

Rewrite $- 1 \cdot (q^{2} i)$ as $- (q^{2} i)$ .

$r = - (q^{2} i) + \frac{- q}{i q}$

Step 3.1.6

Cancel the common factor of $q$ .

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Step 3.1.6.1

Cancel the common factor.

$r = - q^{2} i + \frac{- q}{i q}$

Step 3.1.6.2

Rewrite the expression.

$r = - q^{2} i + \frac{- 1}{i}$

Step 3.1.7

Multiply the numerator and denominator of $\frac{- 1}{i}$ by the conjugate of $i$ to make the denominator real.

$r = - q^{2} i + \frac{- 1}{i} \cdot \frac{i}{i}$

Step 3.1.8

Multiply.

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Step 3.1.8.1

Combine.

$r = - q^{2} i + \frac{- i}{i i}$

Step 3.1.8.2

Simplify the denominator.

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Step 3.1.8.2.1

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

$r = - q^{2} i + \frac{- i}{i^{1} i}$

Step 3.1.8.2.2

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

$r = - q^{2} i + \frac{- i}{i^{1} i^{1}}$

Step 3.1.8.2.3

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

$r = - q^{2} i + \frac{- i}{i^{1 + 1}}$

Step 3.1.8.2.4

Add $1$ and $1$ .

$r = - q^{2} i + \frac{- i}{i^{2}}$

Step 3.1.8.2.5

Rewrite $i^{2}$ as $- 1$ .

$r = - q^{2} i + \frac{- i}{- 1}$

Step 3.1.9

Dividing two negative values results in a positive value.

$r = - q^{2} i + \frac{i}{1}$

Step 3.1.10

Divide $i$ by $1$ .

$r = - q^{2} i + i$