Solve f(x)=x^2-5/x^2+8/x^3

$$f ( x ) = x ^ { 2 } - \frac { 5 } { x ^ { 2 } } + \frac { 8 } { x ^ { 3 } }$$

Evaluate

$$\frac{x^{5}-5x+8}{x^{3}}$$

Short Solution Steps

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

$$\frac{x^{2}x^{2}}{x^{2}}-\frac{5}{x^{2}}+\frac{8}{x^{3}}$$

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

$$\frac{x^{2}x^{2}-5}{x^{2}}+\frac{8}{x^{3}}$$

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

$$\frac{x^{4}-5}{x^{2}}+\frac{8}{x^{3}}$$

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

$$\frac{\left(x^{4}-5\right)x}{x^{3}}+\frac{8}{x^{3}}$$

Since \frac{\left(x^{4}-5\right)x}{x^{3}} and \frac{8}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{4}-5\right)x+8}{x^{3}}$$

Do the multiplications in \left(x^{4}-5\right)x+8.

$$\frac{x^{5}-5x+8}{x^{3}}$$

Factor

$$\frac{x^{5}-5x+8}{x^{3}}$$