Solve 1/x^2-1/9/x-3

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and 9 is 9x^{2}. Multiply \frac{1}{x^{2}} times \frac{9}{9}. Multiply \frac{1}{9} times \frac{x^{2}}{x^{2}}.

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

Since \frac{9}{9x^{2}} and \frac{x^{2}}{9x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Express \frac{\frac{9-x^{2}}{9x^{2}}}{x-3} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x-3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2} and 9 is 9x^{2}. Multiply \frac{1}{x^{2}} times \frac{9}{9}. Multiply \frac{1}{9} times \frac{x^{2}}{x^{2}}.

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

Since \frac{9}{9x^{2}} and \frac{x^{2}}{9x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Express \frac{\frac{9-x^{2}}{9x^{2}}}{x-3} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x-3 in both numerator and denominator.

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