Question

Simplify the rational expression
(3x-9)/(x^(2)-6x+9)
and then find all #s that must be excluded from the domain of the simplified rational expression.
I'm really just having trouble factoring it.

Answer 1

\[\frac{3x-9}{x^2-6x+9}=\frac{3(x-3)}{(x-3)^2}=\frac{3}{x-3}\]

Answer 2

@rrey understand?

Answer 3

Can you explain to me why? I can sort of see it, but I need exact clarification.

Answer 4

do you see why 3x-9 = 3(x-3)?

Answer 5

x^2-6x+9
so we want two numbers that multiply to get 9 but add to get -6
-3 and -3 are two such numbers
x^2-6x+9 = x^2-3x-3x+9 = x(x-3)-3(x-3) = (x-3)(x-3) = (x-3)^2

Answer 6

well for the numerator, I see 3*x is 3x, and 3*-3 is -9
so im not trying to do anything with my positive 3, correct? i'm distributing it

Answer 7

and yeah i udnerstand the bottom prt

Answer 8

My textbook says it is \[\frac{ 3 }{ x-3 }\] am i missing something? @zzr0ck3r