Solve 3/x+2/x^2-5/3ax

$$\frac { 3 } { x } + \frac { 2 } { x ^ { 2 } } - \frac { 5 } { 3 a x }$$

Evaluate

$$\frac{3}{x}-\frac{5}{3ax}+\frac{2}{x^{2}}$$

Short Solution Steps

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

$$\frac{3x}{x^{2}}+\frac{2}{x^{2}}-\frac{5}{3ax}$$

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

$$\frac{3x+2}{x^{2}}-\frac{5}{3ax}$$

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

$$\frac{\left(3x+2\right)\times 3a}{3ax^{2}}-\frac{5x}{3ax^{2}}$$

Since \frac{\left(3x+2\right)\times 3a}{3ax^{2}} and \frac{5x}{3ax^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3x+2\right)\times 3a-5x}{3ax^{2}}$$

Do the multiplications in \left(3x+2\right)\times 3a-5x.

$$\frac{9xa+6a-5x}{3ax^{2}}$$

Factor

$$\frac{\left(\frac{1}{x}\right)^{2}\left(\left(9-\frac{5}{a}\right)x+6\right)}{3}$$