Simplify x/2+2/x

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

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $2 x$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

Reorder the factors of $x \cdot 2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

$\frac{x^{2} + 4}{2 x}$