Solve 3/4m+2/3mn^2-4/n

$$\frac { 3 } { 4 m } + \frac { 2 } { 3 m n ^ { 2 } } - \frac { 4 } { n }$$

Evaluate

$$\frac{3}{4m}-\frac{4}{n}+\frac{2}{3mn^{2}}$$

Short Solution Steps

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

$$\frac{3\times 3n^{2}}{12mn^{2}}+\frac{2\times 4}{12mn^{2}}-\frac{4}{n}$$

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

$$\frac{3\times 3n^{2}+2\times 4}{12mn^{2}}-\frac{4}{n}$$

Do the multiplications in 3\times 3n^{2}+2\times 4.

$$\frac{9n^{2}+8}{12mn^{2}}-\frac{4}{n}$$

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

$$\frac{9n^{2}+8}{12mn^{2}}-\frac{4\times 12mn}{12mn^{2}}$$

Since \frac{9n^{2}+8}{12mn^{2}} and \frac{4\times 12mn}{12mn^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9n^{2}+8-4\times 12mn}{12mn^{2}}$$

Do the multiplications in 9n^{2}+8-4\times 12mn.

$$\frac{9n^{2}+8-48mn}{12mn^{2}}$$

Factor

$$\frac{-\frac{48m}{n}+9+\frac{8}{n^{2}}}{12m}$$