Domain of Equation 2x + 6/x = 18: Finding Valid x Values

Because we have $\frac{6}{x}$ in our equation! When x = 0, this becomes $\frac{6}{0}$, which is undefined in mathematics. Division by zero is impossible.

No! The domain is about which x-values we can input into the expression. It's completely separate from finding what x equals when we solve the equation.

Check every denominator separately! Set each one equal to zero and solve. The domain excludes all values that make any denominator zero.

You can write it as: $x \neq 0$, or in interval notation: $(-\infty, 0) \cup (0, \infty)$, or in words: all real numbers except 0.

$x > 0$ means x can only be positive (like 1, 2, 3...). But $x \neq 0$ means x can be any number except zero - both positive AND negative numbers work!