Solve x-1-12/x-2/x+6+frac{16{x-2}}

$$\frac { x - 1 - \frac { 12 } { x - 2 } } { x + 6 + \frac { 16 } { x - 2 } }$$

Evaluate

$$\frac{x-5}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-1 times \frac{x-2}{x-2}.

$$\frac{\frac{\left(x-1\right)\left(x-2\right)}{x-2}-\frac{12}{x-2}}{x+6+\frac{16}{x-2}}$$

Since \frac{\left(x-1\right)\left(x-2\right)}{x-2} and \frac{12}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-1\right)\left(x-2\right)-12}{x-2}}{x+6+\frac{16}{x-2}}$$

Do the multiplications in \left(x-1\right)\left(x-2\right)-12.

$$\frac{\frac{x^{2}-2x-x+2-12}{x-2}}{x+6+\frac{16}{x-2}}$$

Combine like terms in x^{2}-2x-x+2-12.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{x+6+\frac{16}{x-2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x+6 times \frac{x-2}{x-2}.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{\left(x+6\right)\left(x-2\right)}{x-2}+\frac{16}{x-2}}$$

Since \frac{\left(x+6\right)\left(x-2\right)}{x-2} and \frac{16}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{\left(x+6\right)\left(x-2\right)+16}{x-2}}$$

Do the multiplications in \left(x+6\right)\left(x-2\right)+16.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{x^{2}-2x+6x-12+16}{x-2}}$$

Combine like terms in x^{2}-2x+6x-12+16.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{x^{2}+4x+4}{x-2}}$$

Divide \frac{x^{2}-3x-10}{x-2} by \frac{x^{2}+4x+4}{x-2} by multiplying \frac{x^{2}-3x-10}{x-2} by the reciprocal of \frac{x^{2}+4x+4}{x-2}.

$$\frac{\left(x^{2}-3x-10\right)\left(x-2\right)}{\left(x-2\right)\left(x^{2}+4x+4\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x^{2}-3x-10}{x^{2}+4x+4}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x+2\right)}{\left(x+2\right)^{2}}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-5}{x+2}$$

Expand

$$\frac{x-5}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-1 times \frac{x-2}{x-2}.

$$\frac{\frac{\left(x-1\right)\left(x-2\right)}{x-2}-\frac{12}{x-2}}{x+6+\frac{16}{x-2}}$$

Since \frac{\left(x-1\right)\left(x-2\right)}{x-2} and \frac{12}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-1\right)\left(x-2\right)-12}{x-2}}{x+6+\frac{16}{x-2}}$$

Do the multiplications in \left(x-1\right)\left(x-2\right)-12.

$$\frac{\frac{x^{2}-2x-x+2-12}{x-2}}{x+6+\frac{16}{x-2}}$$

Combine like terms in x^{2}-2x-x+2-12.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{x+6+\frac{16}{x-2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x+6 times \frac{x-2}{x-2}.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{\left(x+6\right)\left(x-2\right)}{x-2}+\frac{16}{x-2}}$$

Since \frac{\left(x+6\right)\left(x-2\right)}{x-2} and \frac{16}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{\left(x+6\right)\left(x-2\right)+16}{x-2}}$$

Do the multiplications in \left(x+6\right)\left(x-2\right)+16.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{x^{2}-2x+6x-12+16}{x-2}}$$

Combine like terms in x^{2}-2x+6x-12+16.

$$\frac{\frac{x^{2}-3x-10}{x-2}}{\frac{x^{2}+4x+4}{x-2}}$$

Divide \frac{x^{2}-3x-10}{x-2} by \frac{x^{2}+4x+4}{x-2} by multiplying \frac{x^{2}-3x-10}{x-2} by the reciprocal of \frac{x^{2}+4x+4}{x-2}.

$$\frac{\left(x^{2}-3x-10\right)\left(x-2\right)}{\left(x-2\right)\left(x^{2}+4x+4\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x^{2}-3x-10}{x^{2}+4x+4}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-5\right)\left(x+2\right)}{\left(x+2\right)^{2}}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-5}{x+2}$$