Solve 2/4x+12/frac{4{2x+6}+1/x+3}

$$\frac { \frac { 2 } { 4 x + 12 } } { \frac { 4 } { 2 x + 6 } + \frac { 1 } { x + 3 } }$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Short Solution Steps

Factor 2x+6.

$$\frac{\frac{2}{4x+12}}{\frac{4}{2\left(x+3\right)}+\frac{1}{x+3}}$$

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

$$\frac{\frac{2}{4x+12}}{\frac{4}{2\left(x+3\right)}+\frac{2}{2\left(x+3\right)}}$$

Since \frac{4}{2\left(x+3\right)} and \frac{2}{2\left(x+3\right)} have the same denominator, add them by adding their numerators. Add 4 and 2 to get 6.

$$\frac{\frac{2}{4x+12}}{\frac{6}{2\left(x+3\right)}}$$

Divide \frac{2}{4x+12} by \frac{6}{2\left(x+3\right)} by multiplying \frac{2}{4x+12} by the reciprocal of \frac{6}{2\left(x+3\right)}.

$$\frac{2\times 2\left(x+3\right)}{\left(4x+12\right)\times 6}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(x+3\right)}{3\left(4x+12\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(x+3\right)}{3\times 4\left(x+3\right)}$$

Cancel out 2\left(x+3\right) in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$