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

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

Evaluate

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

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4k and 2k is 4k. Multiply \frac{1}{2k} times \frac{2}{2}.

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

Since \frac{3}{4k} and \frac{2}{4k} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 3 to get 1.

$$\frac{\frac{1}{4k}}{\frac{1}{3k}+\frac{1}{2k}}$$

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

$$\frac{\frac{1}{4k}}{\frac{2}{6k}+\frac{3}{6k}}$$

Since \frac{2}{6k} and \frac{3}{6k} have the same denominator, add them by adding their numerators. Add 2 and 3 to get 5.

$$\frac{\frac{1}{4k}}{\frac{5}{6k}}$$

Divide \frac{1}{4k} by \frac{5}{6k} by multiplying \frac{1}{4k} by the reciprocal of \frac{5}{6k}.

$$\frac{6k}{4k\times 5}$$

Cancel out 2k in both numerator and denominator.

$$\frac{3}{2\times 5}$$

Multiply 2 and 5 to get 10.

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

Factor

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