Simplify 4/(5x)-(2x)/5

$\frac{4}{5 x} - \frac{2 x}{5}$

Step 1

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

$\frac{4}{5 x} - \frac{2 x}{5} \cdot \frac{x}{x}$

Step 2

Simplify terms.

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

$\frac{4}{5 x} - \frac{2 x \cdot x}{5 x}$

Combine the numerators over the common denominator.

$\frac{4 - 2 x \cdot x}{5 x}$

Step 3

Simplify the numerator.

Factor $2$ out of $4 - 2 x \cdot x$ .

Factor $2$ out of $4$ .

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

Factor $2$ out of $- 2 x \cdot x$ .

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

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

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

$\frac{2 (2 - x^{2})}{5 x}$