Solve n-4/5n-2-5/6n^3

$$\frac { n - 4 } { 5 n - 2 } - \frac { 5 } { 6 n ^ { 3 } }$$

Evaluate

$$\frac{6n^{4}-24n^{3}-25n+10}{6\left(5n-2\right)n^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5n-2 and 6n^{3} is 6\left(5n-2\right)n^{3}. Multiply \frac{n-4}{5n-2} times \frac{6n^{3}}{6n^{3}}. Multiply \frac{5}{6n^{3}} times \frac{5n-2}{5n-2}.

$$\frac{\left(n-4\right)\times 6n^{3}}{6\left(5n-2\right)n^{3}}-\frac{5\left(5n-2\right)}{6\left(5n-2\right)n^{3}}$$

Since \frac{\left(n-4\right)\times 6n^{3}}{6\left(5n-2\right)n^{3}} and \frac{5\left(5n-2\right)}{6\left(5n-2\right)n^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(n-4\right)\times 6n^{3}-5\left(5n-2\right)}{6\left(5n-2\right)n^{3}}$$

Do the multiplications in \left(n-4\right)\times 6n^{3}-5\left(5n-2\right).

$$\frac{6n^{4}-24n^{3}-25n+10}{6\left(5n-2\right)n^{3}}$$

Expand 6\left(5n-2\right)n^{3}.

$$\frac{6n^{4}-24n^{3}-25n+10}{30n^{4}-12n^{3}}$$

Expand

$$\frac{6n^{4}-24n^{3}-25n+10}{6\left(5n-2\right)n^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5n-2 and 6n^{3} is 6\left(5n-2\right)n^{3}. Multiply \frac{n-4}{5n-2} times \frac{6n^{3}}{6n^{3}}. Multiply \frac{5}{6n^{3}} times \frac{5n-2}{5n-2}.

$$\frac{\left(n-4\right)\times 6n^{3}}{6\left(5n-2\right)n^{3}}-\frac{5\left(5n-2\right)}{6\left(5n-2\right)n^{3}}$$

Since \frac{\left(n-4\right)\times 6n^{3}}{6\left(5n-2\right)n^{3}} and \frac{5\left(5n-2\right)}{6\left(5n-2\right)n^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(n-4\right)\times 6n^{3}-5\left(5n-2\right)}{6\left(5n-2\right)n^{3}}$$

Do the multiplications in \left(n-4\right)\times 6n^{3}-5\left(5n-2\right).

$$\frac{6n^{4}-24n^{3}-25n+10}{6\left(5n-2\right)n^{3}}$$

Expand 6\left(5n-2\right)n^{3}.

$$\frac{6n^{4}-24n^{3}-25n+10}{30n^{4}-12n^{3}}$$