Solve f(x)=3x^3-1/2x^2+3/x^3.1=10

$$f ( x ) = 3 x ^ { 3 } - \frac { 1 } { 2 x ^ { 2 } } + \frac { 3 } { x ^ { 3 } } . 1 = 10$$

Evaluate

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

Short Solution Steps

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

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

Since \frac{3x^{3}\times 2x^{2}}{2x^{2}} and \frac{1}{2x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3x^{3}\times 2x^{2}-1.

$$\frac{6x^{5}-1}{2x^{2}}+\frac{3}{x^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x^{2} and x^{3} is 2x^{3}. Multiply \frac{6x^{5}-1}{2x^{2}} times \frac{x}{x}. Multiply \frac{3}{x^{3}} times \frac{2}{2}.

$$\frac{\left(6x^{5}-1\right)x}{2x^{3}}+\frac{3\times 2}{2x^{3}}$$

Since \frac{\left(6x^{5}-1\right)x}{2x^{3}} and \frac{3\times 2}{2x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(6x^{5}-1\right)x+3\times 2}{2x^{3}}$$

Do the multiplications in \left(6x^{5}-1\right)x+3\times 2.

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

Factor

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