Solve f(x)=2x^2-1/x^2+1/x^3

$$f ( x ) = 2 x ^ { 2 } - \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x ^ { 3 } }$$

Evaluate

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

Short Solution Steps

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

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

Since \frac{2x^{2}x^{2}}{x^{2}} and \frac{1}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2x^{2}x^{2}-1.

$$\frac{2x^{4}-1}{x^{2}}+\frac{1}{x^{3}}$$

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{2x^{4}-1}{x^{2}} times \frac{x}{x}.

$$\frac{\left(2x^{4}-1\right)x}{x^{3}}+\frac{1}{x^{3}}$$

Since \frac{\left(2x^{4}-1\right)x}{x^{3}} and \frac{1}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x^{4}-1\right)x+1}{x^{3}}$$

Do the multiplications in \left(2x^{4}-1\right)x+1.

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

Factor

$$\frac{\left(x+1\right)\left(2x^{4}-2x^{3}+2x^{2}-2x+1\right)}{x^{3}}$$