How do you solve? 3x+5x-9 / x(x+3)(2x-5)

Question

finding domain

Answer 1

The domain is the range of x values for which the expression has a definite value.

In this case, the expression isn't defined when the denominator is zero, that is, when:

x(x+3)(2x-5)=0, so that gives us x=0; x+3=0, x=-3; 2x-5=0, 2x=5, x=5/2 (or 2½).

So the domain is x∈(-∞,∞) but x≠0, x≠-3, x≠5/2.

This can be written x∈{(-∞,-3), (-3,0), (0,5/2), (5/2,∞)}.