Solve 4/x^2(2x)-5/x^21

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

Evaluate

$$\frac{8x-5}{x^{2}}$$

Short Solution Steps

Express \frac{4}{x^{2}}\times 2 as a single fraction.

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

Express \frac{4\times 2}{x^{2}}x as a single fraction.

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

Cancel out x in both numerator and denominator.

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

Express \frac{5}{x^{2}}\times 1 as a single fraction.

$$\frac{2\times 4}{x}-\frac{5}{x^{2}}$$

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

$$\frac{2\times 4x}{x^{2}}-\frac{5}{x^{2}}$$

Since \frac{2\times 4x}{x^{2}} and \frac{5}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 4x-5}{x^{2}}$$

Do the multiplications in 2\times 4x-5.

$$\frac{8x-5}{x^{2}}$$

Factor

$$\frac{8x-5}{x^{2}}$$