Simplify 4/15+18/x

$\frac{4}{15} + \frac{18}{x}$

Step 1

To write $\frac{4}{15}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{4}{15} \cdot \frac{x}{x} + \frac{18}{x}$

Step 2

To write $\frac{18}{x}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{4}{15} \cdot \frac{x}{x} + \frac{18}{x} \cdot \frac{15}{15}$

Step 3

Write each expression with a common denominator of $15 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{15}$ by $\frac{x}{x}$ .

$\frac{4 x}{15 x} + \frac{18}{x} \cdot \frac{15}{15}$

Multiply $\frac{18}{x}$ by $\frac{15}{15}$ .

$\frac{4 x}{15 x} + \frac{18 \cdot 15}{x \cdot 15}$

Reorder the factors of $x \cdot 15$ .

$\frac{4 x}{15 x} + \frac{18 \cdot 15}{15 x}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 x + 18 \cdot 15}{15 x}$

Step 5

Simplify the numerator.

Factor $2$ out of $4 x + 18 \cdot 15$ .

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) + 18 \cdot 15}{15 x}$

Factor $2$ out of $18 \cdot 15$ .

$\frac{2 (2 x) + 2 (9 \cdot 15)}{15 x}$

Factor $2$ out of $2 (2 x) + 2 (9 \cdot 15)$ .

$\frac{2 (2 x + 9 \cdot 15)}{15 x}$

Multiply $9$ by $15$ .

$\frac{2 (2 x + 135)}{15 x}$