Solve 5/x^3-2/x^2-1/x+200

$$\frac{ 5 }{ { x }^{ 3 } } - \frac{ 2 }{ { x }^{ 2 } } - \frac{ 1 }{ x } +200$$

Evaluate

$$200-\frac{1}{x}-\frac{2}{x^{2}}+\frac{5}{x^{3}}$$

Short Solution Steps

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

$$\frac{5}{x^{3}}-\frac{2x}{x^{3}}-\frac{1}{x}+200$$

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

$$\frac{5-2x}{x^{3}}-\frac{1}{x}+200$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{3} and x is x^{3}. Multiply \frac{1}{x} times \frac{x^{2}}{x^{2}}.

$$\frac{5-2x}{x^{3}}-\frac{x^{2}}{x^{3}}+200$$

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

$$\frac{5-2x-x^{2}}{x^{3}}+200$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 200 times \frac{x^{3}}{x^{3}}.

$$\frac{5-2x-x^{2}}{x^{3}}+\frac{200x^{3}}{x^{3}}$$

Since \frac{5-2x-x^{2}}{x^{3}} and \frac{200x^{3}}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{5-2x-x^{2}+200x^{3}}{x^{3}}$$

Factor

$$\frac{200x^{3}-x^{2}-2x+5}{x^{3}}$$