Solve 2x/x+5-3x-2/2(x+5)

$$\frac { 2 x } { x + 5 } - \frac { 3 x - 2 } { 2 ( x + 5 ) }$$

Evaluate

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

Short Solution Steps

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

$$\frac{2\times 2x}{2\left(x+5\right)}-\frac{3x-2}{2\left(x+5\right)}$$

Since \frac{2\times 2x}{2\left(x+5\right)} and \frac{3x-2}{2\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2x-\left(3x-2\right)}{2\left(x+5\right)}$$

Do the multiplications in 2\times 2x-\left(3x-2\right).

$$\frac{4x-3x+2}{2\left(x+5\right)}$$

Combine like terms in 4x-3x+2.

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

Expand 2\left(x+5\right).

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

Expand

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

Short Solution Steps

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

$$\frac{2\times 2x}{2\left(x+5\right)}-\frac{3x-2}{2\left(x+5\right)}$$

Since \frac{2\times 2x}{2\left(x+5\right)} and \frac{3x-2}{2\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2x-\left(3x-2\right)}{2\left(x+5\right)}$$

Do the multiplications in 2\times 2x-\left(3x-2\right).

$$\frac{4x-3x+2}{2\left(x+5\right)}$$

Combine like terms in 4x-3x+2.

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

Expand 2\left(x+5\right).

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