Question 693780
To simplify {{{(x^2-9)/(2x+6)}}}, you start by factoring numerator and denominator.
In the denominator, you can take out {{{2}}} as a common factor:
{{{2x+6=2(x+3)}}}
The numerator is a difference of squares, which is one of those special products you must have been taught about, maybe as
{{{(a+b)(a-b)=a^2-b^2}}}.
So {{{x^2-9=(x+3)(x-3)}}}.
 
If {{{x=3}}}, the denominator is zero, and {{{(x^2-9)/(2x+6)}}} does not exist, it is undefined. {{{x}}} not = {{{0}}} is your restriction on the variable.
 
For any other value of {{{x}}},
{{{(x^2-9)/(2x+6)=cross((x+3))(x-3)/2cross((x+3))=highlight((x-3)/2)}}}.
 
NOTE: You can write {{{(x^2-9)/(2x+6)}}} as (x^2-9)/(2x+6).
The parentheses are implied by the long horizontal fraction line in {{{(x^2-9)/(2x+6)}}},
but you need to write them out in (x^2-9)/(2x+6),
because otherwise you have
x^2-9/2x+6 = {{{x^2-9/2x+6}}}.