Evaluate the limit: _x 2 (x2 + 3x - 10)/(x - 2)

$$\frac{2^2 + 3(2) - 10}{2 - 2} = \frac{4 + 6 - 10}{0} = \frac{0}{0}$$

Since this is an indeterminate form, we need to simplify the expression.

We need two numbers that multiply to $-10$ and add to 3. These numbers are 5 and $-2$.

$$x^2 + 3x - 10 = (x+5)(x-2)$$

This is valid because $x \to 2$ means $x$ is approaching 2 but is not equal to 2, so $x-2 \neq 0$.

$$\lim_{x \to 2} (x+5)$$

$$2+5 = 7$$

The final answer is 7.