You can put this solution on YOUR website!
(Please put parentheses around numerators and denominators in the future.)
Assuming your functions are:
(g o f)(x) means g(f(x)). So
The domain will be all Real numbers except those that make any of these denominators zero.
First let's look at the "little" denominators. They are both x-2. I hope it is clear that x=2 would make x-2 zero. (If not, then set x-2 = 0 and solve.) So we must exclude 2 from the domain.
The "big" denominator is
. This is a fraction and if we understand fractions well we know that they are zero only if the numerator is zero. So x=0 would make
equal to zero. (If this is not clear, then set
and solve.) SO we must exclude x=0 from the domain, too.
So the domain of g(f(x)) is all Real numbers except 0 and 2.