Simplify 4/x-(5x)/2

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

Step 1

To write $\frac{4}{x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

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

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

Step 3

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

Multiply $\frac{4}{x}$ by $\frac{2}{2}$ .

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

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

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

Reorder the factors of $x \cdot 2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{8 - 5 x \cdot x}{2 x}$

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

Move $x$ .

$\frac{8 - 5 (x \cdot x)}{2 x}$

Multiply $x$ by $x$ .

$\frac{8 - 5 x^{2}}{2 x}$