Solve 3/2n-4/n^2+2/5n

$$\frac { 3 } { 2 n } - \frac { 4 } { n ^ { 2 } } + \frac { 2 } { 5 n }$$

Evaluate

$$\frac{19}{10n}-\frac{4}{n^{2}}$$

Short Solution Steps

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

$$\frac{3n}{2n^{2}}-\frac{4\times 2}{2n^{2}}+\frac{2}{5n}$$

Since \frac{3n}{2n^{2}} and \frac{4\times 2}{2n^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3n-4\times 2}{2n^{2}}+\frac{2}{5n}$$

Do the multiplications in 3n-4\times 2.

$$\frac{3n-8}{2n^{2}}+\frac{2}{5n}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2n^{2} and 5n is 10n^{2}. Multiply \frac{3n-8}{2n^{2}} times \frac{5}{5}. Multiply \frac{2}{5n} times \frac{2n}{2n}.

$$\frac{5\left(3n-8\right)}{10n^{2}}+\frac{2\times 2n}{10n^{2}}$$

Since \frac{5\left(3n-8\right)}{10n^{2}} and \frac{2\times 2n}{10n^{2}} have the same denominator, add them by adding their numerators.

$$\frac{5\left(3n-8\right)+2\times 2n}{10n^{2}}$$

Do the multiplications in 5\left(3n-8\right)+2\times 2n.

$$\frac{15n-40+4n}{10n^{2}}$$

Combine like terms in 15n-40+4n.

$$\frac{19n-40}{10n^{2}}$$

Factor

$$\frac{19n-40}{10n^{2}}$$