Solve x^2/2+4x/1+3/x=

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

Evaluate

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

Short Solution Steps

Anything divided by one gives itself.

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

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

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

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

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

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

$$\frac{x^{2}+8x}{2}+\frac{3}{x}$$

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

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

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

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

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

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

Factor

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