Solve x^2-9x+18/x^2-5x+6+x-3/x^2-5x+6

$$\frac { x ^ { 2 } - 9 x + 18 } { x ^ { 2 } - 5 x + 6 } + \frac { x - 3 } { x ^ { 2 } - 5 x + 6 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-9x+18}{x^{2}-5x+6}.

$$\frac{\left(x-6\right)\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}+\frac{x-3}{x^{2}-5x+6}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x-6}{x-2}+\frac{x-3}{x^{2}-5x+6}$$

Factor the expressions that are not already factored in \frac{x-3}{x^{2}-5x+6}.

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

Cancel out x-3 in both numerator and denominator.

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

Since \frac{x-6}{x-2} and \frac{1}{x-2} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-6+1.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-9x+18}{x^{2}-5x+6}.

$$\frac{\left(x-6\right)\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}+\frac{x-3}{x^{2}-5x+6}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x-6}{x-2}+\frac{x-3}{x^{2}-5x+6}$$

Factor the expressions that are not already factored in \frac{x-3}{x^{2}-5x+6}.

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

Cancel out x-3 in both numerator and denominator.

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

Since \frac{x-6}{x-2} and \frac{1}{x-2} have the same denominator, add them by adding their numerators.

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

Combine like terms in x-6+1.

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