Find the smallest integer $x$ where the expression $\frac{\sqrt{x-2}}{x^2+x-6}$ is defined.
To find the smallest integer $x$ where the expression is defined, I need to consider two things: the square root in the numerator and the denominator. The square root in the numerator is only defined when the radicand, $x-2$, is non-negative, so I need $x \geq 2$. The denominator is a quadratic expression that can be factored as $(x+3)(x-2)$. The denominator cannot be zero, so I need to avoid the values $x=-3$ and $x=2$. Therefore, the smallest integer $x$ that satisfies both conditions is $x=3$. 