Solve 2/x+2x/3-3x/2

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

Evaluate

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

Short Solution Steps

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

$$\frac{2\times 3}{3x}+\frac{2xx}{3x}-\frac{3x}{2}$$

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

$$\frac{2\times 3+2xx}{3x}-\frac{3x}{2}$$

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

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

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

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

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

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

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

$$\frac{12+4x^{2}-9x^{2}}{6x}$$

Combine like terms in 12+4x^{2}-9x^{2}.

$$\frac{12-5x^{2}}{6x}$$

Factor

$$\frac{12-5x^{2}}{6x}$$