Answer
When simplified, the answer is
[tex]\frac{-5x+17}{x^2-5x+6}[/tex]Explanation
[2/x² - 5x + 6] - [5/x - 2]
[tex]\frac{2}{x^2-5x+6}-\frac{5}{x-2}[/tex]To solve this, we need to first factorize x² - 5x + 6
x² - 5x + 6
= x² - 3x - 2x + 6
= x (x - 3) - 2 (x - 3)
= (x - 3) (x - 2)
So, we can rewrite the question, and then take an LCM
[tex]\begin{gathered} \frac{2}{x^2-5x+6}-\frac{5}{x-2} \\ \frac{2}{(x-3)(x-2)}-\frac{5}{x-2} \end{gathered}[/tex]We will then take the LCM
[tex]\begin{gathered} \frac{2}{(x-3)(x-2)}-\frac{5}{x-2} \\ =\frac{2-5(x-3)}{(x-3)(x-2)} \\ =\frac{2-5x+15}{(x-3)(x-2)} \\ =\frac{-5x+17}{(x-3)(x-2)} \\ =\frac{-5x+17}{x^2-5x+6} \end{gathered}[/tex]Hope this Helps!!!
