Basic Math Examples

$\frac{2 q + q}{4 q} - \frac{3 q}{q^{4}}$

Step 1

Add $2 q$ and $q$ .

$\frac{3 q}{4 q} - \frac{3 q}{q^{4}}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $q$ .

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Step 2.1.1

Cancel the common factor.

$\frac{3 q}{4 q} - \frac{3 q}{q^{4}}$

Step 2.1.2

Rewrite the expression.

$\frac{3}{4} - \frac{3 q}{q^{4}}$

Step 2.2

Cancel the common factor of $q$ and $q^{4}$ .

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Step 2.2.1

Factor $q$ out of $3 q$ .

$\frac{3}{4} - \frac{q \cdot 3}{q^{4}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $q$ out of $q^{4}$ .

$\frac{3}{4} - \frac{q \cdot 3}{q \cdot q^{3}}$

Step 2.2.2.2

Cancel the common factor.

$\frac{3}{4} - \frac{q \cdot 3}{q \cdot q^{3}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{3}{4} - \frac{3}{q^{3}}$

Step 3

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{q^{3}}{q^{3}}$ .

$\frac{3}{4} \cdot \frac{q^{3}}{q^{3}} - \frac{3}{q^{3}}$

Step 4

To write $- \frac{3}{q^{3}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} \cdot \frac{q^{3}}{q^{3}} - \frac{3}{q^{3}} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of $4 q^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{3}{4}$ by $\frac{q^{3}}{q^{3}}$ .

$\frac{3 q^{3}}{4 q^{3}} - \frac{3}{q^{3}} \cdot \frac{4}{4}$

Step 5.2

Multiply $\frac{3}{q^{3}}$ by $\frac{4}{4}$ .

$\frac{3 q^{3}}{4 q^{3}} - \frac{3 \cdot 4}{q^{3} \cdot 4}$

Step 5.3

Reorder the factors of $q^{3} \cdot 4$ .

$\frac{3 q^{3}}{4 q^{3}} - \frac{3 \cdot 4}{4 q^{3}}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 q^{3} - 3 \cdot 4}{4 q^{3}}$

Step 7

Simplify the numerator.

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Step 7.1

Factor $3$ out of $3 q^{3} - 3 \cdot 4$ .

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Step 7.1.1

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

$\frac{3 (q^{3}) - 3 \cdot 4}{4 q^{3}}$

Step 7.1.2

Factor $3$ out of $- 3 \cdot 4$ .

$\frac{3 (q^{3}) + 3 (- 1 \cdot 4)}{4 q^{3}}$

Step 7.1.3

Factor $3$ out of $3 (q^{3}) + 3 (- 1 \cdot 4)$ .

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

Step 7.2

Multiply $- 1$ by $4$ .

$\frac{3 (q^{3} - 4)}{4 q^{3}}$