SOLUTION: What is the domain of {{{x/(x^2-5x+6)}}}? my work (x-2)=2 (x-3)=3 Check: {{{2^2-5(2)+6=0}}} 0=0 {{{3^2-5(3)+6=0}}} 0=0 x cannot equal 2, x cannot equal 3 I'm not

Question 697269: What is the domain of ?
my work
(x-2)=2
(x-3)=3
Check:
0=0
0=0
x cannot equal 2, x cannot equal 3
I'm not sure if this is the domain.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You are correct. So the domain in set-builder notation would be

$\{x|x\in \mathbb{R},x \neq 2, x \neq 3\}$

This basically says "x can be any real number BUT it cannot be 2 and it cannot be 3"

In interval notation, the domain is $(-\infty,2)\cup(2,3)\cup(3,\infty)$

This says the same thing more or less but now we're talking about the interval $(-\infty,\infty)$ , but we're "poking" holes in this interval at x = 2 and x = 3 when we write what's above.
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