Solve x-x/x+3/x+2

$$\frac { x - \frac { x } { x + 3 } } { x + 2 }$$

Evaluate

$$\frac{x}{x+3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+3}{x+3}.

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

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

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

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

$$\frac{\frac{x^{2}+3x-x}{x+3}}{x+2}$$

Combine like terms in x^{2}+3x-x.

$$\frac{\frac{x^{2}+2x}{x+3}}{x+2}$$

Express \frac{\frac{x^{2}+2x}{x+3}}{x+2} as a single fraction.

$$\frac{x^{2}+2x}{\left(x+3\right)\left(x+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x}{x+3}$$

Expand

$$\frac{x}{x+3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x+3}{x+3}.

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

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

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

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

$$\frac{\frac{x^{2}+3x-x}{x+3}}{x+2}$$

Combine like terms in x^{2}+3x-x.

$$\frac{\frac{x^{2}+2x}{x+3}}{x+2}$$

Express \frac{\frac{x^{2}+2x}{x+3}}{x+2} as a single fraction.

$$\frac{x^{2}+2x}{\left(x+3\right)\left(x+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x}{x+3}$$