Solve x/9-1/x/1+frac{3{x}}

$$\frac { \frac { x } { 9 } - \frac { 1 } { x } } { 1 + \frac { 3 } { x } }$$

Evaluate

$$\frac{x-3}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and x is 9x. Multiply \frac{x}{9} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{9}{9}.

$$\frac{\frac{xx}{9x}-\frac{9}{9x}}{1+\frac{3}{x}}$$

Since \frac{xx}{9x} and \frac{9}{9x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-9}{9x}}{1+\frac{3}{x}}$$

Do the multiplications in xx-9.

$$\frac{\frac{x^{2}-9}{9x}}{1+\frac{3}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x^{2}-9}{9x}}{\frac{x}{x}+\frac{3}{x}}$$

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

$$\frac{\frac{x^{2}-9}{9x}}{\frac{x+3}{x}}$$

Divide \frac{x^{2}-9}{9x} by \frac{x+3}{x} by multiplying \frac{x^{2}-9}{9x} by the reciprocal of \frac{x+3}{x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(x+3\right)}{9\left(x+3\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x-3}{9}$$

Expand

$$\frac{x}{9}-\frac{1}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and x is 9x. Multiply \frac{x}{9} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{9}{9}.

$$\frac{\frac{xx}{9x}-\frac{9}{9x}}{1+\frac{3}{x}}$$

Since \frac{xx}{9x} and \frac{9}{9x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{xx-9}{9x}}{1+\frac{3}{x}}$$

Do the multiplications in xx-9.

$$\frac{\frac{x^{2}-9}{9x}}{1+\frac{3}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x^{2}-9}{9x}}{\frac{x}{x}+\frac{3}{x}}$$

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

$$\frac{\frac{x^{2}-9}{9x}}{\frac{x+3}{x}}$$

Divide \frac{x^{2}-9}{9x} by \frac{x+3}{x} by multiplying \frac{x^{2}-9}{9x} by the reciprocal of \frac{x+3}{x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(x+3\right)}{9\left(x+3\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x-3}{9}$$