Solve (1-81/x^2)/(1-frac{9{x})}

$$\frac { ( 1 - \frac { 81 } { x ^ { 2 } } ) } { ( 1 - \frac { 9 } { x } ) }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{x^{2}}{x^{2}}-\frac{81}{x^{2}}}{1-\frac{9}{x}}$$

Since \frac{x^{2}}{x^{2}} and \frac{81}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-81}{x^{2}}}{1-\frac{9}{x}}$$

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

$$\frac{\frac{x^{2}-81}{x^{2}}}{\frac{x}{x}-\frac{9}{x}}$$

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

$$\frac{\frac{x^{2}-81}{x^{2}}}{\frac{x-9}{x}}$$

Divide \frac{x^{2}-81}{x^{2}} by \frac{x-9}{x} by multiplying \frac{x^{2}-81}{x^{2}} by the reciprocal of \frac{x-9}{x}.

$$\frac{\left(x^{2}-81\right)x}{x^{2}\left(x-9\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}-81}{x\left(x-9\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-9 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{x^{2}}{x^{2}}-\frac{81}{x^{2}}}{1-\frac{9}{x}}$$

Since \frac{x^{2}}{x^{2}} and \frac{81}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-81}{x^{2}}}{1-\frac{9}{x}}$$

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

$$\frac{\frac{x^{2}-81}{x^{2}}}{\frac{x}{x}-\frac{9}{x}}$$

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

$$\frac{\frac{x^{2}-81}{x^{2}}}{\frac{x-9}{x}}$$

Divide \frac{x^{2}-81}{x^{2}} by \frac{x-9}{x} by multiplying \frac{x^{2}-81}{x^{2}} by the reciprocal of \frac{x-9}{x}.

$$\frac{\left(x^{2}-81\right)x}{x^{2}\left(x-9\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}-81}{x\left(x-9\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-9 in both numerator and denominator.

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