Solve 1/2/x+1+1/2/x^2+x+1

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

Evaluate

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

Short Solution Steps

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+1\right) and 2\left(x^{2}+x+1\right) is 2\left(x+1\right)\left(x^{2}+x+1\right). Multiply \frac{1}{2\left(x+1\right)} times \frac{x^{2}+x+1}{x^{2}+x+1}. Multiply \frac{1}{2\left(x^{2}+x+1\right)} times \frac{x+1}{x+1}.

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

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

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

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

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

Expand 2\left(x+1\right)\left(x^{2}+x+1\right).

$$\frac{x^{2}+2x+2}{2x^{3}+4x^{2}+4x+2}$$

Factor

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