Trigonometry Examples

$\frac{10}{p q} + \frac{4}{q}$

Step 1

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

$\frac{10}{p q} + \frac{4}{q} \cdot \frac{p}{p}$

Step 2

Write each expression with a common denominator of $p q$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{4}{q}$ by $\frac{p}{p}$ .

$\frac{10}{p q} + \frac{4 p}{q p}$

Step 2.2

Reorder the factors of $q p$ .

$\frac{10}{p q} + \frac{4 p}{p q}$

Step 3

Combine the numerators over the common denominator.

$\frac{10 + 4 p}{p q}$

Step 4

Factor $2$ out of $10 + 4 p$ .

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Step 4.1

Factor $2$ out of $10$ .

$\frac{2 (5) + 4 p}{p q}$

Step 4.2

Factor $2$ out of $4 p$ .

$\frac{2 (5) + 2 (2 p)}{p q}$

Step 4.3

Factor $2$ out of $2 (5) + 2 (2 p)$ .

$\frac{2 (5 + 2 p)}{p q}$