Which of the following expressions is equivalent to
$$ \left[1 \quad – \quad\dfrac{(n!)^2}{(n+1)!(n-1)!}\right]$$ where $n>2$ and $n! = n(n-1)(n-2)\cdots 3 \cdot 2 \cdot 1$ ?

1. $\quad \dfrac{n-2}{n+1}$
2. $\quad \dfrac{1}{n+1}$
3. $\quad \dfrac{2}{n^2-1}$
4. $\quad \dfrac{1}{n-1}$
5. $\quad \dfrac{n}{n+1}$

If $2x-3y=1$, $x+2y=4$, and $y=-2$ are equations that represent sides $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$ of triangle $ABC$ in the coordinate plane, what are the coordinates of the mid-point of side $\overline{BC}$?

1. $\quad (4, 0)$
2. $\quad (4, -1)$
3. $\quad \left(\dfrac{9}{2}, -\dfrac{1}{4}\right)$
4. $\quad \left(5, -\dfrac{1}{2}\right)$
5. $\quad (5, -1)$

For all values of $x$ where the expression is defined
$$ \dfrac{\dfrac{x-5}{x-2}}{\dfrac{1}{3}-\dfrac{1}{x-2}}=?$$

1. $\quad -3$
2. $\quad 3$
3. $\quad 3(x-5)$
4. $\quad \dfrac{x-2}{3(x-5)}$
5. $\quad \dfrac{(x-5)^2}{3(x-2)^2}$