Solve f(x)=x-6/2x^2-15x+18+x-5/15-13x+2x^2

$$f ( x ) = \frac { x - 6 } { 2 x ^ { 2 } - 15 x + 18 } + \frac { x - 5 } { 15 - 13 x + 2 x ^ { 2 } }$$

Evaluate

$$\frac{2}{2x-3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x-6}{2x^{2}-15x+18}.

$$\frac{x-6}{\left(x-6\right)\left(2x-3\right)}+\frac{x-5}{15-13x+2x^{2}}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{1}{2x-3}+\frac{x-5}{15-13x+2x^{2}}$$

Factor the expressions that are not already factored in \frac{x-5}{15-13x+2x^{2}}.

$$\frac{1}{2x-3}+\frac{x-5}{\left(x-5\right)\left(2x-3\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{1}{2x-3}+\frac{1}{2x-3}$$

Combine \frac{1}{2x-3} and \frac{1}{2x-3} to get 2\times \frac{1}{2x-3}.

$$2\times \frac{1}{2x-3}$$

Express 2\times \frac{1}{2x-3} as a single fraction.

$$\frac{2}{2x-3}$$

Expand

$$\frac{2}{2x-3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x-6}{2x^{2}-15x+18}.

$$\frac{x-6}{\left(x-6\right)\left(2x-3\right)}+\frac{x-5}{15-13x+2x^{2}}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{1}{2x-3}+\frac{x-5}{15-13x+2x^{2}}$$

Factor the expressions that are not already factored in \frac{x-5}{15-13x+2x^{2}}.

$$\frac{1}{2x-3}+\frac{x-5}{\left(x-5\right)\left(2x-3\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{1}{2x-3}+\frac{1}{2x-3}$$

Combine \frac{1}{2x-3} and \frac{1}{2x-3} to get 2\times \frac{1}{2x-3}.

$$2\times \frac{1}{2x-3}$$

Express 2\times \frac{1}{2x-3} as a single fraction.

$$\frac{2}{2x-3}$$