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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x-1}{x-1}.

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

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

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

Do the multiplications in 9+9\left(x-1\right).

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

Combine like terms in 9+9x-9.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x+1}{x+1}.

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

Since \frac{9}{x+1} and \frac{9\left(x+1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 9-9\left(x+1\right).

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

Combine like terms in 9-9x-9.

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

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

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

Cancel out 9x in both numerator and denominator.

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

To find the opposite of x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x-1}{x-1}.

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

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

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

Do the multiplications in 9+9\left(x-1\right).

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

Combine like terms in 9+9x-9.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{x+1}{x+1}.

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

Since \frac{9}{x+1} and \frac{9\left(x+1\right)}{x+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 9-9\left(x+1\right).

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

Combine like terms in 9-9x-9.

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

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

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

Cancel out 9x in both numerator and denominator.

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

To find the opposite of x-1, find the opposite of each term.

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

The opposite of -1 is 1.

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