Domain of (x+8) / (x (x+10))

The domain of this, assuming it's a function, is all real numbers such that x does not equal zero or negative ten.

In interval notation, this is (-∞, - 10) U (-10, 0) U (0, ∞).

In set builder notation, this is x ≠ - 10, x ≠ 0.

These inputs are excluded from the domain because they would otherwise allow division by zero. Try plugging in one of the restricted inputs. You'll see that it does not work! On a graph of this function, you will see vertical asymptotes.