SOLUTION: help with a question how to find the domain of f(x)/g(x) g(x)= x+2/x-4 f(x)=x^2+6 x^2 + 6 / x+2/x-4 I believe that I have to multiply both sides by x-4 but I am reall

Question 407687: help with a question
how to find the domain of f(x)/g(x) g(x)= x+2/x-4 f(x)=x^2+6

x^2 + 6 / x+2/x-4
I believe that I have to multiply both sides by x-4
but I am really lost on a problem like this and do not understand.
Answer by graphmatics(170) (Show Source): You can put this solution on YOUR website!
f(x)/g(x) = ((x+2)/(x-4))/((x^2+6)/(1))
f(x)/g(x) = ((x+2)/(x-4))*(1)/(x^2+6)
= ((x+2)*(1))/((x-4)*(x^2+6))
a point is not in the domain if (x-4)*(x^2+6) = 0.
This is because dividing by 0 is undefined.
x^2+6 > 0 for each x. If x = 4 then (4-4)*(x^2+6) = 0
so the domain is every x except x = 4

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