Solve (1-1/x+2)+x^2+2x+1/x+2

$$( 1 - \frac { 1 } { x + 2 } ) + \frac { x ^ { 2 } + 2 x + 1 } { x + 2 }$$

Evaluate

$$x+1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

$$\frac{x+2}{x+2}-\frac{1}{x+2}+\frac{x^{2}+2x+1}{x+2}$$

Since \frac{x+2}{x+2} and \frac{1}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2-1}{x+2}+\frac{x^{2}+2x+1}{x+2}$$

Combine like terms in x+2-1.

$$\frac{x+1}{x+2}+\frac{x^{2}+2x+1}{x+2}$$

Since \frac{x+1}{x+2} and \frac{x^{2}+2x+1}{x+2} have the same denominator, add them by adding their numerators.

$$\frac{x+1+x^{2}+2x+1}{x+2}$$

Combine like terms in x+1+x^{2}+2x+1.

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

Factor the expressions that are not already factored in \frac{3x+2+x^{2}}{x+2}.

$$\frac{\left(x+1\right)\left(x+2\right)}{x+2}$$

Cancel out x+2 in both numerator and denominator.

$$x+1$$

Expand

$$x+1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

$$\frac{x+2}{x+2}-\frac{1}{x+2}+\frac{x^{2}+2x+1}{x+2}$$

Since \frac{x+2}{x+2} and \frac{1}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2-1}{x+2}+\frac{x^{2}+2x+1}{x+2}$$

Combine like terms in x+2-1.

$$\frac{x+1}{x+2}+\frac{x^{2}+2x+1}{x+2}$$

Since \frac{x+1}{x+2} and \frac{x^{2}+2x+1}{x+2} have the same denominator, add them by adding their numerators.

$$\frac{x+1+x^{2}+2x+1}{x+2}$$

Combine like terms in x+1+x^{2}+2x+1.

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

Factor the expressions that are not already factored in \frac{3x+2+x^{2}}{x+2}.

$$\frac{\left(x+1\right)\left(x+2\right)}{x+2}$$

Cancel out x+2 in both numerator and denominator.

$$x+1$$