Solve x+5/8-x+x^2-17x+70/x^2-18x+80

$$\frac { x + 5 } { 8 - x } + \frac { x ^ { 2 } - 17 x + 70 } { x ^ { 2 } - 18 x + 80 }$$

Evaluate

$$\frac{12}{8-x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-17x+70}{x^{2}-18x+80}.

$$\frac{x+5}{8-x}+\frac{\left(x-10\right)\left(x-7\right)}{\left(x-10\right)\left(x-8\right)}$$

Cancel out x-10 in both numerator and denominator.

$$\frac{x+5}{8-x}+\frac{x-7}{x-8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8-x and x-8 is x-8. Multiply \frac{x+5}{8-x} times \frac{-1}{-1}.

$$\frac{-\left(x+5\right)}{x-8}+\frac{x-7}{x-8}$$

Since \frac{-\left(x+5\right)}{x-8} and \frac{x-7}{x-8} have the same denominator, add them by adding their numerators.

$$\frac{-\left(x+5\right)+x-7}{x-8}$$

Do the multiplications in -\left(x+5\right)+x-7.

$$\frac{-x-5+x-7}{x-8}$$

Combine like terms in -x-5+x-7.

$$\frac{-12}{x-8}$$

Expand

$$-\frac{12}{x-8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-17x+70}{x^{2}-18x+80}.

$$\frac{x+5}{8-x}+\frac{\left(x-10\right)\left(x-7\right)}{\left(x-10\right)\left(x-8\right)}$$

Cancel out x-10 in both numerator and denominator.

$$\frac{x+5}{8-x}+\frac{x-7}{x-8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8-x and x-8 is x-8. Multiply \frac{x+5}{8-x} times \frac{-1}{-1}.

$$\frac{-\left(x+5\right)}{x-8}+\frac{x-7}{x-8}$$

Since \frac{-\left(x+5\right)}{x-8} and \frac{x-7}{x-8} have the same denominator, add them by adding their numerators.

$$\frac{-\left(x+5\right)+x-7}{x-8}$$

Do the multiplications in -\left(x+5\right)+x-7.

$$\frac{-x-5+x-7}{x-8}$$

Combine like terms in -x-5+x-7.

$$\frac{-12}{x-8}$$