Solve 3/x^2+5/x-2x

$$\frac{ 3 }{ { x }^{ 2 } } + \frac{ 5 }{ x } -2x$$

Evaluate

$$-2x+\frac{5}{x}+\frac{3}{x^{2}}$$

Short Solution Steps

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

$$\frac{3}{x^{2}}+\frac{5x}{x^{2}}-2x$$

Since \frac{3}{x^{2}} and \frac{5x}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3+5x}{x^{2}}-2x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x times \frac{x^{2}}{x^{2}}.

$$\frac{3+5x}{x^{2}}+\frac{-2xx^{2}}{x^{2}}$$

Since \frac{3+5x}{x^{2}} and \frac{-2xx^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3+5x-2xx^{2}}{x^{2}}$$

Do the multiplications in 3+5x-2xx^{2}.

$$\frac{3+5x-2x^{3}}{x^{2}}$$

Factor

$$\frac{\left(x+1\right)\left(3+2x-2x^{2}\right)}{x^{2}}$$