Solve x^4/4+3x^2/2-2-3/x+6/x^3

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Since \frac{x^{4}+6x^{2}}{4} and \frac{2\times 4}{4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{4}+6x^{2}-2\times 4.

$$\frac{x^{4}+6x^{2}-8}{4}-\frac{3}{x}+\frac{6}{x^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{x^{4}+6x^{2}-8}{4} times \frac{x}{x}. Multiply \frac{3}{x} times \frac{4}{4}.

$$\frac{\left(x^{4}+6x^{2}-8\right)x}{4x}-\frac{3\times 4}{4x}+\frac{6}{x^{3}}$$

Since \frac{\left(x^{4}+6x^{2}-8\right)x}{4x} and \frac{3\times 4}{4x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x^{4}+6x^{2}-8\right)x-3\times 4}{4x}+\frac{6}{x^{3}}$$

Do the multiplications in \left(x^{4}+6x^{2}-8\right)x-3\times 4.

$$\frac{x^{5}+6x^{3}-8x-12}{4x}+\frac{6}{x^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4x and x^{3} is 4x^{3}. Multiply \frac{x^{5}+6x^{3}-8x-12}{4x} times \frac{x^{2}}{x^{2}}. Multiply \frac{6}{x^{3}} times \frac{4}{4}.

$$\frac{\left(x^{5}+6x^{3}-8x-12\right)x^{2}}{4x^{3}}+\frac{6\times 4}{4x^{3}}$$

Since \frac{\left(x^{5}+6x^{3}-8x-12\right)x^{2}}{4x^{3}} and \frac{6\times 4}{4x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{5}+6x^{3}-8x-12\right)x^{2}+6\times 4}{4x^{3}}$$

Do the multiplications in \left(x^{5}+6x^{3}-8x-12\right)x^{2}+6\times 4.

$$\frac{x^{7}+6x^{5}-8x^{3}-12x^{2}+24}{4x^{3}}$$

Factor

$$\frac{x^{7}+6x^{5}-8x^{3}-12x^{2}+24}{4x^{3}}$$