Simplify 1/x+(2x)/5

$\frac{1}{x} + \frac{2 x}{5}$

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{x} \cdot \frac{5}{5} + \frac{2 x}{5}$

To write $\frac{2 x}{5}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{x} \cdot \frac{5}{5} + \frac{2 x}{5} \cdot \frac{x}{x}$

Write each expression with a common denominator of $x \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x}$ by $\frac{5}{5}$ .

$\frac{5}{x \cdot 5} + \frac{2 x}{5} \cdot \frac{x}{x}$

Multiply $\frac{2 x}{5}$ by $\frac{x}{x}$ .

$\frac{5}{x \cdot 5} + \frac{2 x \cdot x}{5 x}$

Reorder the factors of $x \cdot 5$ .

$\frac{5}{5 x} + \frac{2 x \cdot x}{5 x}$

Combine the numerators over the common denominator.

$\frac{5 + 2 x \cdot x}{5 x}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{5 + 2 (x \cdot x)}{5 x}$

Multiply $x$ by $x$ .

$\frac{5 + 2 x^{2}}{5 x}$