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1. Sum of vertical asymptotes ●○○○○ 10 ptsThe graph of $y=\frac{5x^2-9}{3x^2+5x+2}$ has vertical asymptotes at $x = a$ and $x = b$. Find $a + b$. Round to two decimal places.
2. Ratio of alternating sums ●○○○○ 10 ptsFind the value of $\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}$ as a fraction in lowest terms. Give the numerator and the denominator.
3. Sum of common divisors ●○○○○ 10 ptsFind the sum of all positive divisors of $50$ that are also divisors of $15$.
4. Ratio of alternating power-of-two sums ●○○○○ 10 ptsCompute $\dfrac{2+4-8+16+32-64}{4+8-16+32+64-128}$. Give your answer as a decimal.
5. Complex solutions of a rational equation ●●○○○ 20 ptsFind the number of complex solutions to $\frac{z^3 - 1}{z^2 + z - 2} = 0$.
6. Positive integers giving a hole ●●○○○ 20 ptsFind the number of positive integers $n$ for which the graph of $y = \frac{(x + 3)(x - 7)^5}{(x - 1)(x - 7)^n}$ has a hole at $x = 7$.
7. Sizes of two sets from subset counts ●●○○○ 20 ptsLet $A$ and $B$ be two finite sets. The number of subsets of $A$ minus the number of subsets of $B$ is $112$. Find the number of elements in $A$ and in $B$.
8. Equation with reciprocals of linear factors ●●○○○ 20 ptsFind the roots of $\frac{1}{x+4} - \frac{1}{x-7} = \frac{11}{30}$, with $x \neq -4$ and $x \neq 7$.
9. Difference of fractions equals one ●●○○○ 20 ptsFind all values of $x$ (with $x \neq 0, 1, -1$) for which $\frac{1}{x^2 - x} - \frac{1}{x^3 - x} = 1$. Round each value to two decimal places.
10. Fractional-power equation with substitution ●●○○○ 20 ptsSolve the equation $(x - 2)^{2/3} + (x - 2)^{1/3} - 2 = 0$, using real cube roots.

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