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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{3}-x^{2}+2x times \frac{x}{x}.

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

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

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

Do the multiplications in \left(3x^{3}-x^{2}+2x\right)x+2.

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

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{3x^{4}-x^{3}+2x^{2}+2}{x} times \frac{x}{x}.

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

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

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

Do the multiplications in \left(3x^{4}-x^{3}+2x^{2}+2\right)x-1.

$$\frac{3x^{5}-x^{4}+2x^{3}+2x-1}{x^{2}}+\frac{3}{x^{3}}$$

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{3x^{5}-x^{4}+2x^{3}+2x-1}{x^{2}} times \frac{x}{x}.

$$\frac{\left(3x^{5}-x^{4}+2x^{3}+2x-1\right)x}{x^{3}}+\frac{3}{x^{3}}$$

Since \frac{\left(3x^{5}-x^{4}+2x^{3}+2x-1\right)x}{x^{3}} and \frac{3}{x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x^{5}-x^{4}+2x^{3}+2x-1\right)x+3}{x^{3}}$$

Do the multiplications in \left(3x^{5}-x^{4}+2x^{3}+2x-1\right)x+3.

$$\frac{3x^{6}-x^{5}+2x^{4}+2x^{2}-x+3}{x^{3}}$$

Factor

$$\frac{3x^{6}-x^{5}+2x^{4}+2x^{2}-x+3}{x^{3}}$$