Solve 2*5/2x-10/(x+2)=

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

Evaluate

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

Short Solution Steps

Express 2\times \frac{5}{2x} as a single fraction.

$$\frac{2\times 5}{2x}-\frac{10}{x+2}$$

Cancel out 2 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x+2 is x\left(x+2\right). Multiply \frac{5}{x} times \frac{x+2}{x+2}. Multiply \frac{10}{x+2} times \frac{x}{x}.

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

Since \frac{5\left(x+2\right)}{x\left(x+2\right)} and \frac{10x}{x\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 5\left(x+2\right)-10x.

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

Combine like terms in 5x+10-10x.

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

Expand x\left(x+2\right).

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

Factor

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