Solve x+1/x-6-5/frac{x+1{x-6}+8}

$$\frac { \frac { x + 1 } { x - 6 } - 5 } { \frac { x + 1 } { x - 6 } + 8 }$$

Evaluate

$$\frac{31-4x}{9x-47}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x-6}{x-6}.

$$\frac{\frac{x+1}{x-6}-\frac{5\left(x-6\right)}{x-6}}{\frac{x+1}{x-6}+8}$$

Since \frac{x+1}{x-6} and \frac{5\left(x-6\right)}{x-6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+1-5\left(x-6\right)}{x-6}}{\frac{x+1}{x-6}+8}$$

Do the multiplications in x+1-5\left(x-6\right).

$$\frac{\frac{x+1-5x+30}{x-6}}{\frac{x+1}{x-6}+8}$$

Combine like terms in x+1-5x+30.

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1}{x-6}+8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x-6}{x-6}.

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1}{x-6}+\frac{8\left(x-6\right)}{x-6}}$$

Since \frac{x+1}{x-6} and \frac{8\left(x-6\right)}{x-6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1+8\left(x-6\right)}{x-6}}$$

Do the multiplications in x+1+8\left(x-6\right).

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1+8x-48}{x-6}}$$

Combine like terms in x+1+8x-48.

$$\frac{\frac{-4x+31}{x-6}}{\frac{9x-47}{x-6}}$$

Divide \frac{-4x+31}{x-6} by \frac{9x-47}{x-6} by multiplying \frac{-4x+31}{x-6} by the reciprocal of \frac{9x-47}{x-6}.

$$\frac{\left(-4x+31\right)\left(x-6\right)}{\left(x-6\right)\left(9x-47\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{-4x+31}{9x-47}$$

Expand

$$\frac{31-4x}{9x-47}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x-6}{x-6}.

$$\frac{\frac{x+1}{x-6}-\frac{5\left(x-6\right)}{x-6}}{\frac{x+1}{x-6}+8}$$

Since \frac{x+1}{x-6} and \frac{5\left(x-6\right)}{x-6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x+1-5\left(x-6\right)}{x-6}}{\frac{x+1}{x-6}+8}$$

Do the multiplications in x+1-5\left(x-6\right).

$$\frac{\frac{x+1-5x+30}{x-6}}{\frac{x+1}{x-6}+8}$$

Combine like terms in x+1-5x+30.

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1}{x-6}+8}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8 times \frac{x-6}{x-6}.

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1}{x-6}+\frac{8\left(x-6\right)}{x-6}}$$

Since \frac{x+1}{x-6} and \frac{8\left(x-6\right)}{x-6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1+8\left(x-6\right)}{x-6}}$$

Do the multiplications in x+1+8\left(x-6\right).

$$\frac{\frac{-4x+31}{x-6}}{\frac{x+1+8x-48}{x-6}}$$

Combine like terms in x+1+8x-48.

$$\frac{\frac{-4x+31}{x-6}}{\frac{9x-47}{x-6}}$$

Divide \frac{-4x+31}{x-6} by \frac{9x-47}{x-6} by multiplying \frac{-4x+31}{x-6} by the reciprocal of \frac{9x-47}{x-6}.

$$\frac{\left(-4x+31\right)\left(x-6\right)}{\left(x-6\right)\left(9x-47\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{-4x+31}{9x-47}$$