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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Multiply $x$ by $x$ .

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

Apply the distributive property.

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

Multiply $5$ by $- 2$ .

$\frac{x^{2} + 5 x - 10}{x (x - 2)}$