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

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

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $5$ .

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

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

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

Multiply $5$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Apply the distributive property.

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

Move $5$ to the left of $x$ .

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

Multiply $- 2$ by $5$ .

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

Apply the distributive property.

$\frac{5 x - 10 + (- x - 1 \cdot 2) \cdot 2}{10}$

Multiply $- 1$ by $2$ .

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

Apply the distributive property.

$\frac{5 x - 10 - x \cdot 2 - 2 \cdot 2}{10}$

Multiply $2$ by $- 1$ .

$\frac{5 x - 10 - 2 x - 2 \cdot 2}{10}$

Multiply $- 2$ by $2$ .

$\frac{5 x - 10 - 2 x - 4}{10}$

Subtract $2 x$ from $5 x$ .

$\frac{3 x - 10 - 4}{10}$

Subtract $4$ from $- 10$ .

$\frac{3 x - 14}{10}$