SOLUTION: Given the functions, {{{ f(x) = x-4 }}} and {{{ g(x)=(x+2)/(x-2) }}}, determine an expression for h(x) such that {{{ h(x)=(f*g/g)(x) }}}. Having trouble with this practice quest

Question 949689: Given the functions, and , determine an expression for h(x) such that .
Having trouble with this practice question, please help.
Thank you
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Plug everything in and simplify. Just fitting the formula shown and some algebra steps.

Here is the raw unsimplified form:

Examine that expression to see how it is made.
The numerator is the composition as shown in that part for h(x).
The denominator is as shown in that other part of .

The most important thing to be able is to form that expression for h(x) as defined. The next thing to do is to simplify that expression.
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