Solve (4/5x-7/8x):1/x^2

$$( \frac { 4 } { 5 x } - \frac { 7 } { 8 x } ) : \frac { 1 } { x ^ { 2 } }$$

Evaluate

$$-\frac{3x}{40}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x and 8x is 40x. Multiply \frac{4}{5x} times \frac{8}{8}. Multiply \frac{7}{8x} times \frac{5}{5}.

$$\frac{\frac{4\times 8}{40x}-\frac{7\times 5}{40x}}{\frac{1}{x^{2}}}$$

Since \frac{4\times 8}{40x} and \frac{7\times 5}{40x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4\times 8-7\times 5}{40x}}{\frac{1}{x^{2}}}$$

Do the multiplications in 4\times 8-7\times 5.

$$\frac{\frac{32-35}{40x}}{\frac{1}{x^{2}}}$$

Do the calculations in 32-35.

$$\frac{\frac{-3}{40x}}{\frac{1}{x^{2}}}$$

Divide \frac{-3}{40x} by \frac{1}{x^{2}} by multiplying \frac{-3}{40x} by the reciprocal of \frac{1}{x^{2}}.

$$\frac{-3x^{2}}{40x}$$

Cancel out x in both numerator and denominator.

$$\frac{-3x}{40}$$

Expand

$$-\frac{3x}{40}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x and 8x is 40x. Multiply \frac{4}{5x} times \frac{8}{8}. Multiply \frac{7}{8x} times \frac{5}{5}.

$$\frac{\frac{4\times 8}{40x}-\frac{7\times 5}{40x}}{\frac{1}{x^{2}}}$$

Since \frac{4\times 8}{40x} and \frac{7\times 5}{40x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4\times 8-7\times 5}{40x}}{\frac{1}{x^{2}}}$$

Do the multiplications in 4\times 8-7\times 5.

$$\frac{\frac{32-35}{40x}}{\frac{1}{x^{2}}}$$

Do the calculations in 32-35.

$$\frac{\frac{-3}{40x}}{\frac{1}{x^{2}}}$$

Divide \frac{-3}{40x} by \frac{1}{x^{2}} by multiplying \frac{-3}{40x} by the reciprocal of \frac{1}{x^{2}}.

$$\frac{-3x^{2}}{40x}$$

Cancel out x in both numerator and denominator.

$$\frac{-3x}{40}$$