Solve x+3/2/1+23/x+4x/1

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

Evaluate

$$5x+\frac{3}{2}+\frac{6}{x}$$

Short Solution Steps

Anything divided by one gives itself.

$$x+\frac{3}{2}+2\times \frac{3}{x}+\frac{4x}{1}$$

Express 2\times \frac{3}{x} as a single fraction.

$$x+\frac{3}{2}+\frac{2\times 3}{x}+\frac{4x}{1}$$

Anything divided by one gives itself.

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

Combine x and 4x to get 5x.

$$5x+\frac{3}{2}+\frac{2\times 3}{x}$$

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

$$5x+\frac{3x}{2x}+\frac{2\times 2\times 3}{2x}$$

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

$$5x+\frac{3x+2\times 2\times 3}{2x}$$

Do the multiplications in 3x+2\times 2\times 3.

$$5x+\frac{3x+12}{2x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x times \frac{2x}{2x}.

$$\frac{5x\times 2x}{2x}+\frac{3x+12}{2x}$$

Since \frac{5x\times 2x}{2x} and \frac{3x+12}{2x} have the same denominator, add them by adding their numerators.

$$\frac{5x\times 2x+3x+12}{2x}$$

Do the multiplications in 5x\times 2x+3x+12.

$$\frac{10x^{2}+3x+12}{2x}$$

Factor

$$\frac{10x^{2}+3x+12}{2x}$$