Question

Simplify [2/x²-5x+6] - [5/x-2]

Answer 1

When simplified, the answer is

`(-5x+17)/(x^2-5x+6)`

Step-by-step explanation

[2/x² - 5x + 6] - [5/x - 2​]

`(2)/(x^2-5x+6)-(5)/(x-2)`

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

`\begin{gathered} (2)/(x^2-5x+6)-(5)/(x-2) \\ (2)/((x-3)(x-2))-(5)/(x-2) \end{gathered}`

We will then take the LCM

`\begin{gathered} (2)/((x-3)(x-2))-(5)/(x-2) \\ =(2-5(x-3))/((x-3)(x-2)) \\ =(2-5x+15)/((x-3)(x-2)) \\ =(-5x+17)/((x-3)(x-2)) \\ =(-5x+17)/(x^2-5x+6) \end{gathered}`

Hope this Helps!!!