Solve 1/2+2/frac{x{3}+1}

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

Evaluate

$$\frac{x+15}{2\left(x+3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

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

Since \frac{x}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

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

Divide 2 by \frac{x+3}{3} by multiplying 2 by the reciprocal of \frac{x+3}{3}.

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

Multiply 2 and 3 to get 6.

$$\frac{1}{2}+\frac{6}{x+3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x+3 is 2\left(x+3\right). Multiply \frac{1}{2} times \frac{x+3}{x+3}. Multiply \frac{6}{x+3} times \frac{2}{2}.

$$\frac{x+3}{2\left(x+3\right)}+\frac{6\times 2}{2\left(x+3\right)}$$

Since \frac{x+3}{2\left(x+3\right)} and \frac{6\times 2}{2\left(x+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{x+3+6\times 2}{2\left(x+3\right)}$$

Do the multiplications in x+3+6\times 2.

$$\frac{x+3+12}{2\left(x+3\right)}$$

Combine like terms in x+3+12.

$$\frac{x+15}{2\left(x+3\right)}$$

Expand 2\left(x+3\right).

$$\frac{x+15}{2x+6}$$

Factor

$$\frac{x+15}{2\left(x+3\right)}$$