Solve 3/2x-1/x+3/x^2

$$\frac { 3 } { 2 x } - \frac { 1 } { x } + \frac { 3 } { x ^ { 2 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and x is 2x. Multiply \frac{1}{x} times \frac{2}{2}.

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

Since \frac{3}{2x} and \frac{2}{2x} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from 3 to get 1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and x^{2} is 2x^{2}. Multiply \frac{1}{2x} times \frac{x}{x}. Multiply \frac{3}{x^{2}} times \frac{2}{2}.

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

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

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

Do the multiplications in x+3\times 2.

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

Factor

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