Before plugging in $x=2$, see if you can factor the numerator $x^2 - 3x - 10$ and cancel any common factors with the denominator $x-5$ (as long as the denominator is not zero).

When you compute the numerator after substitution or after simplifying, pay close attention to negative signs: subtracting a negative and dividing by a negative can change the sign of the final result.

If you evaluate $h(2)$ directly from the original fraction, try also evaluating it from a simplified form of $h(x)$ and make sure both approaches give the same value.

In a new expression line, type (2^2 - 3*2 - 10)/(2 - 5) exactly as the function definition with $x=2$. Desmos will show a single numeric output to the right; that value is $h(2)$.

In one line, type (x^2 - 3x - 10)/(x - 5) and let Desmos graph it. In a second line, type y = x + 2. Notice that the graphs overlap except at $x=5$. Now either:

• Add a table to the first expression and enter 2 in the $x$-column, or
• Type 2 + 2 in a new line. The resulting numeric output is the value of $h(2)$.

The question is asking you to evaluate the function $h(x)$ at $x=2$.

That means you should replace every $x$ in

with $2$ and simplify, or simplify the function first and then substitute $x=2$.

Factor the quadratic in the numerator:

So for $x \neq 5$,

Now cancel the common factor $(x-5)$ in the numerator and denominator (this is allowed as long as $x \neq 5$):

Now use the simplified form $h(x) = x + 2$ for $x \neq 5$.

Substitute $x=2$:

Evaluate the sum:

So $h(2) = 4$, which corresponds to choice D.