SOLUTION: {{{f(x)= (3x^2-6)/(x^2-4x)}}} {{{h(x)= 6x+2}}} find the domain of f(h(x)) I have no clue thanks bunches for help

Question 547282:

find the domain of f(h(x))
I have no clue thanks bunches for help

Answer by mathie123(224) (Show Source): You can put this solution on YOUR website!
To find f(h(x)), we need to plug in h(x) for any x we see in f(x). This leaves:

We could expand this... though it is not needed and will take some time. Instead, we know that there is no limitations on x in the numerator. But we do know that when there is a fraction, the denominator cannot be equal to 0.
This means that
cannot equal 0.
Well... when does this expression equal 0. In other words, lets solve:

Again, we can expand this, or we could see that each term has a common factor of (6x+2) and factor this out. This leaves:

If two things multiply to give a product of 0, then at least one of them must be 0. This means

This means x can be anything except and .
Hopefully this helps! Please let me know if you still do not understand:)
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