Final answer:
The function (x+2)/(x³-4x) is equivalent to 1/(x*(x-2)) for all x in the domain, excluding x=0, x=2, and x=-2 where the denominator equals zero.
Step-by-step explanation:
The function (x+2)/(x³-4x) given in the question can be simplified, which makes it more understandable. First, let's factor the denominator to get x(x²-4). This can be further factored into x(x-2)(x+2) by applying the difference of squares method. The original function thus becomes:
(x+2)/(x*(x-2)*(x+2)).
As you can see, (x+2) appears in both the numerator and the denominator, so it cancels out. The function, equivalent for all x in the domain, except where the denominator equals zero (x=0, x=-2, x=2), is then:
1/(x*(x-2)).
Learn more about Equivalent Functions