Solve 1+1/x+2/x-frac{a{a}}=

$$\frac { 1 + \frac { 1 } { x + 2 } } { x - \frac { a } { a } } =$$

Evaluate

$$\frac{x+3}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

Divide a by a to get 1.

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

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

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

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

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

Combine like terms in x+2+1.

$$\frac{\frac{x+3}{x+2}}{x-1}$$

Express \frac{\frac{x+3}{x+2}}{x-1} as a single fraction.

$$\frac{x+3}{\left(x+2\right)\left(x-1\right)}$$

Apply the distributive property by multiplying each term of x+2 by each term of x-1.

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

Combine -x and 2x to get x.

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

Expand

$$\frac{x+3}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

Divide a by a to get 1.

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

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

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

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

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

Combine like terms in x+2+1.

$$\frac{\frac{x+3}{x+2}}{x-1}$$

Express \frac{\frac{x+3}{x+2}}{x-1} as a single fraction.

$$\frac{x+3}{\left(x+2\right)\left(x-1\right)}$$

Apply the distributive property by multiplying each term of x+2 by each term of x-1.

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

Combine -x and 2x to get x.

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