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

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

Evaluate

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

Short Solution Steps

Express \frac{\frac{x+3}{x}}{x-\frac{9}{x}} as a single fraction.

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

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

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

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

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

Do the multiplications in xx-9.

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

Cancel out x and x.

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

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Express \frac{\frac{x+3}{x}}{x-\frac{9}{x}} as a single fraction.

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

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

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

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

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

Do the multiplications in xx-9.

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

Cancel out x and x.

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

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

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