Solve 12/x^4-x^3/2+x^2

$$\frac{ 12 }{ { x }^{ 4 } } - \frac{ { x }^{ 3 } }{ 2 } + { x }^{ 2 }$$

Evaluate

$$-\frac{x^{3}}{2}+x^{2}+\frac{12}{x^{4}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{4} and 2 is 2x^{4}. Multiply \frac{12}{x^{4}} times \frac{2}{2}. Multiply \frac{x^{3}}{2} times \frac{x^{4}}{x^{4}}.

$$\frac{12\times 2}{2x^{4}}-\frac{x^{3}x^{4}}{2x^{4}}+x^{2}$$

Since \frac{12\times 2}{2x^{4}} and \frac{x^{3}x^{4}}{2x^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12\times 2-x^{3}x^{4}}{2x^{4}}+x^{2}$$

Do the multiplications in 12\times 2-x^{3}x^{4}.

$$\frac{24-x^{7}}{2x^{4}}+x^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{2x^{4}}{2x^{4}}.

$$\frac{24-x^{7}}{2x^{4}}+\frac{x^{2}\times 2x^{4}}{2x^{4}}$$

Since \frac{24-x^{7}}{2x^{4}} and \frac{x^{2}\times 2x^{4}}{2x^{4}} have the same denominator, add them by adding their numerators.

$$\frac{24-x^{7}+x^{2}\times 2x^{4}}{2x^{4}}$$

Do the multiplications in 24-x^{7}+x^{2}\times 2x^{4}.

$$\frac{24-x^{7}+2x^{6}}{2x^{4}}$$

Factor

$$-\frac{\frac{1}{2}\left(x^{7}-2x^{6}-24\right)}{x^{4}}$$