SOLUTION: For the given functions f and g, find the following: f(x)=2x/x-2 and g(x)=x-2/x+4. Also find the domain. (f/g)(x)

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Question 1131212: For the given functions f and g, find the following: f(x)=2x/x-2 and g(x)=x-2/x+4. Also find the domain.
(f/g)(x)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2x%2F%28x-2%29 and
g%28x%29=%28x-2%29%2F%28x%2B4%29+

%28f%2Fg%29%28x%29+=f%28x%29%2Fg%28x%29

f%28x%29%2Fg%28x%29=%282x%2F%28x-2%29%29%2F%28%28x-2%29%2F%28x%2B4%29+%29



f%28x%29%2Fg%28x%29=%282x%28x%2B4%29%29%2F%28%28x-2%29%28x-2%29%29

f%28x%29%2Fg%28x%29=%282x%28x%2B4%29%29%2F%28x-2%29%5E2

the domain:
exclude values of x that make original denominator %28x-2%29%2F%28x%2B4%29+=0
%28x-2%29=0=>x=2
%28x%2B4%29=0=>x=-4

so, domain will be:
{ x element R: x%3C%3E-4 and x%3C%3E2 }