Solve 3/3b-1/2b/frac{2{3b}+4/4b}

$$\frac { \frac { 3 } { 3 b } - \frac { 1 } { 2 b } } { \frac { 2 } { 3 b } + \frac { 4 } { 4 b } }$$

Evaluate

$$\frac{3}{10}=0.3$$

Short Solution Steps

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

$$\frac{\frac{3\times 2}{6b}-\frac{3}{6b}}{\frac{2}{3b}+\frac{4}{4b}}$$

Since \frac{3\times 2}{6b} and \frac{3}{6b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3\times 2-3}{6b}}{\frac{2}{3b}+\frac{4}{4b}}$$

Do the multiplications in 3\times 2-3.

$$\frac{\frac{6-3}{6b}}{\frac{2}{3b}+\frac{4}{4b}}$$

Do the calculations in 6-3.

$$\frac{\frac{3}{6b}}{\frac{2}{3b}+\frac{4}{4b}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3b and 4b is 12b. Multiply \frac{2}{3b} times \frac{4}{4}. Multiply \frac{4}{4b} times \frac{3}{3}.

$$\frac{\frac{3}{6b}}{\frac{2\times 4}{12b}+\frac{4\times 3}{12b}}$$

Since \frac{2\times 4}{12b} and \frac{4\times 3}{12b} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{6b}}{\frac{2\times 4+4\times 3}{12b}}$$

Do the multiplications in 2\times 4+4\times 3.

$$\frac{\frac{3}{6b}}{\frac{8+12}{12b}}$$

Do the calculations in 8+12.

$$\frac{\frac{3}{6b}}{\frac{20}{12b}}$$

Divide \frac{3}{6b} by \frac{20}{12b} by multiplying \frac{3}{6b} by the reciprocal of \frac{20}{12b}.

$$\frac{3\times 12b}{6b\times 20}$$

Cancel out 2\times 2\times 3b in both numerator and denominator.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$