The functions f and h are defined as follows:
f(x) = (x + 5)/(x - 7) and h(x) = (x + 5)(x - 7).
Explain why the functions f and h are not the same function.
The two functions f(x) and h(x) can only possibly be equal if (x + 5) and (x - 7) are both equal to one. This is clearly impossible. Function h(x) is taking a product of the two binomials, while function f(x) seeks the quotient.
In simpler terms, one is multiplying them, while the other is dividing them.