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

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

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

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

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

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

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

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

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

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

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

Reorder the factors of $(2 - x) x$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 4$ by $2$ .

$\frac{5 x - 8 - 4 (- x)}{x (2 - x)}$

Multiply $- 1$ by $- 4$ .

$\frac{5 x - 8 + 4 x}{x (2 - x)}$

Add $5 x$ and $4 x$ .

$\frac{9 x - 8}{x (2 - x)}$