Solve x/3x+6-1/6x+12+x+12/12x+24=

$$\frac { x } { 3 x + 6 } - \frac { 1 } { 6 x + 12 } + \frac { x + 12 } { 12 x + 24 } =$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Short Solution Steps

Factor 3x+6. Factor 6x+12.

$$\frac{x}{3\left(x+2\right)}-\frac{1}{6\left(x+2\right)}+\frac{x+12}{12x+24}$$

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

$$\frac{2x}{6\left(x+2\right)}-\frac{1}{6\left(x+2\right)}+\frac{x+12}{12x+24}$$

Since \frac{2x}{6\left(x+2\right)} and \frac{1}{6\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x-1}{6\left(x+2\right)}+\frac{x+12}{12x+24}$$

Factor 12x+24.

$$\frac{2x-1}{6\left(x+2\right)}+\frac{x+12}{12\left(x+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6\left(x+2\right) and 12\left(x+2\right) is 12\left(x+2\right). Multiply \frac{2x-1}{6\left(x+2\right)} times \frac{2}{2}.

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

Since \frac{2\left(2x-1\right)}{12\left(x+2\right)} and \frac{x+12}{12\left(x+2\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\left(2x-1\right)+x+12.

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

Combine like terms in 4x-2+x+12.

$$\frac{5x+10}{12\left(x+2\right)}$$

Factor the expressions that are not already factored in \frac{5x+10}{12\left(x+2\right)}.

$$\frac{5\left(x+2\right)}{12\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$