Solve x-7/x+6-7/frac{x-7{x+6}+6}

$$\frac { \frac { x - 7 } { x + 6 } - 7 } { \frac { x - 7 } { x + 6 } + 6 }$$

Evaluate

$$-\frac{6x+49}{7x+29}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{x+6}{x+6}.

$$\frac{\frac{x-7}{x+6}-\frac{7\left(x+6\right)}{x+6}}{\frac{x-7}{x+6}+6}$$

Since \frac{x-7}{x+6} and \frac{7\left(x+6\right)}{x+6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-7-7\left(x+6\right)}{x+6}}{\frac{x-7}{x+6}+6}$$

Do the multiplications in x-7-7\left(x+6\right).

$$\frac{\frac{x-7-7x-42}{x+6}}{\frac{x-7}{x+6}+6}$$

Combine like terms in x-7-7x-42.

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7}{x+6}+6}$$

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

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7}{x+6}+\frac{6\left(x+6\right)}{x+6}}$$

Since \frac{x-7}{x+6} and \frac{6\left(x+6\right)}{x+6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7+6\left(x+6\right)}{x+6}}$$

Do the multiplications in x-7+6\left(x+6\right).

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7+6x+36}{x+6}}$$

Combine like terms in x-7+6x+36.

$$\frac{\frac{-6x-49}{x+6}}{\frac{7x+29}{x+6}}$$

Divide \frac{-6x-49}{x+6} by \frac{7x+29}{x+6} by multiplying \frac{-6x-49}{x+6} by the reciprocal of \frac{7x+29}{x+6}.

$$\frac{\left(-6x-49\right)\left(x+6\right)}{\left(x+6\right)\left(7x+29\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{-6x-49}{7x+29}$$

Expand

$$-\frac{6x+49}{7x+29}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{x+6}{x+6}.

$$\frac{\frac{x-7}{x+6}-\frac{7\left(x+6\right)}{x+6}}{\frac{x-7}{x+6}+6}$$

Since \frac{x-7}{x+6} and \frac{7\left(x+6\right)}{x+6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-7-7\left(x+6\right)}{x+6}}{\frac{x-7}{x+6}+6}$$

Do the multiplications in x-7-7\left(x+6\right).

$$\frac{\frac{x-7-7x-42}{x+6}}{\frac{x-7}{x+6}+6}$$

Combine like terms in x-7-7x-42.

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7}{x+6}+6}$$

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

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7}{x+6}+\frac{6\left(x+6\right)}{x+6}}$$

Since \frac{x-7}{x+6} and \frac{6\left(x+6\right)}{x+6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7+6\left(x+6\right)}{x+6}}$$

Do the multiplications in x-7+6\left(x+6\right).

$$\frac{\frac{-6x-49}{x+6}}{\frac{x-7+6x+36}{x+6}}$$

Combine like terms in x-7+6x+36.

$$\frac{\frac{-6x-49}{x+6}}{\frac{7x+29}{x+6}}$$

Divide \frac{-6x-49}{x+6} by \frac{7x+29}{x+6} by multiplying \frac{-6x-49}{x+6} by the reciprocal of \frac{7x+29}{x+6}.

$$\frac{\left(-6x-49\right)\left(x+6\right)}{\left(x+6\right)\left(7x+29\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{-6x-49}{7x+29}$$