Solve 9+1/x/9-frac{9{x^2}}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x}{x}.

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

Since \frac{9x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x^{2}}{x^{2}}.

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

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

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

Divide \frac{9x+1}{x} by \frac{9x^{2}-9}{x^{2}} by multiplying \frac{9x+1}{x} by the reciprocal of \frac{9x^{2}-9}{x^{2}}.

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

Cancel out x in both numerator and denominator.

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

Use the distributive property to multiply x by 9x+1.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x}{x}.

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

Since \frac{9x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x^{2}}{x^{2}}.

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

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

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

Divide \frac{9x+1}{x} by \frac{9x^{2}-9}{x^{2}} by multiplying \frac{9x+1}{x} by the reciprocal of \frac{9x^{2}-9}{x^{2}}.

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

Cancel out x in both numerator and denominator.

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

Use the distributive property to multiply x by 9x+1.

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