Solve x+8/x-9+8/frac{x+8{x-9}-9}

$$\frac { \frac { x + 8 } { x - 9 } + 8 } { \frac { x + 8 } { x - 9 } - 9 }$$

Evaluate

$$\frac{9x-64}{89-8x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x-9}{x-9}.

$$\frac{\frac{x+8}{x-9}+\frac{8\left(x-9\right)}{x-9}}{\frac{x+8}{x-9}-9}$$

Since \frac{x+8}{x-9} and \frac{8\left(x-9\right)}{x-9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+8+8\left(x-9\right)}{x-9}}{\frac{x+8}{x-9}-9}$$

Do the multiplications in x+8+8\left(x-9\right).

$$\frac{\frac{x+8+8x-72}{x-9}}{\frac{x+8}{x-9}-9}$$

Combine like terms in x+8+8x-72.

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8}{x-9}-9}$$

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

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8}{x-9}-\frac{9\left(x-9\right)}{x-9}}$$

Since \frac{x+8}{x-9} and \frac{9\left(x-9\right)}{x-9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8-9\left(x-9\right)}{x-9}}$$

Do the multiplications in x+8-9\left(x-9\right).

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8-9x+81}{x-9}}$$

Combine like terms in x+8-9x+81.

$$\frac{\frac{9x-64}{x-9}}{\frac{-8x+89}{x-9}}$$

Divide \frac{9x-64}{x-9} by \frac{-8x+89}{x-9} by multiplying \frac{9x-64}{x-9} by the reciprocal of \frac{-8x+89}{x-9}.

$$\frac{\left(9x-64\right)\left(x-9\right)}{\left(x-9\right)\left(-8x+89\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{9x-64}{-8x+89}$$

Expand

$$\frac{9x-64}{89-8x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x-9}{x-9}.

$$\frac{\frac{x+8}{x-9}+\frac{8\left(x-9\right)}{x-9}}{\frac{x+8}{x-9}-9}$$

Since \frac{x+8}{x-9} and \frac{8\left(x-9\right)}{x-9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x+8+8\left(x-9\right)}{x-9}}{\frac{x+8}{x-9}-9}$$

Do the multiplications in x+8+8\left(x-9\right).

$$\frac{\frac{x+8+8x-72}{x-9}}{\frac{x+8}{x-9}-9}$$

Combine like terms in x+8+8x-72.

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8}{x-9}-9}$$

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

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8}{x-9}-\frac{9\left(x-9\right)}{x-9}}$$

Since \frac{x+8}{x-9} and \frac{9\left(x-9\right)}{x-9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8-9\left(x-9\right)}{x-9}}$$

Do the multiplications in x+8-9\left(x-9\right).

$$\frac{\frac{9x-64}{x-9}}{\frac{x+8-9x+81}{x-9}}$$

Combine like terms in x+8-9x+81.

$$\frac{\frac{9x-64}{x-9}}{\frac{-8x+89}{x-9}}$$

Divide \frac{9x-64}{x-9} by \frac{-8x+89}{x-9} by multiplying \frac{9x-64}{x-9} by the reciprocal of \frac{-8x+89}{x-9}.

$$\frac{\left(9x-64\right)\left(x-9\right)}{\left(x-9\right)\left(-8x+89\right)}$$

Cancel out x-9 in both numerator and denominator.

$$\frac{9x-64}{-8x+89}$$