1. $\dfrac{4(4)+2}{6}\Rightarrow \dfrac{16+2}{6}\Rightarrow \dfrac{18}{6}\Rightarrow 3$
2. $\dfrac{-2-3}{3(-2)-9}\Rightarrow \dfrac{-5}{-6-9}\Rightarrow \dfrac{-5}{-15}\Rightarrow \dfrac{1}{3}$
3. $\dfrac{-4-3}{(-4)^2-4(-4)+3}\Rightarrow \dfrac{-7}{16+16+3}\Rightarrow -\dfrac{7}{35}\Rightarrow -\dfrac{1}{5}$
4. $\dfrac{-1+2}{(-1)^2+3(-1)+2}\Rightarrow \dfrac{1}{1-3+2}\Rightarrow \dfrac{1}{0}\Rightarrow \text{Undefined}$
5. $\dfrac{\cancel{b}+2}{\cancel{b^2+4b}+4}\Rightarrow \dfrac{2}{4}\Rightarrow \dfrac{1}{2}$
6. $\dfrac{(4)^2-4-6}{4-3}\Rightarrow \dfrac{16-10}{1}\Rightarrow \dfrac{6}{1} \Rightarrow 6$
7. $\phantom{a}$
$\begin{array}[t]{rrrrr} k&+&10&\neq &0 \\ &-&10&&-10 \\ \hline &&k&\neq &-10 \end{array}$
8. $\phantom{a}$
$\begin{array}[t]{rrrrr} &&18p(p&-&2) \\ \\ &&18p&\neq &0 \\ &&p&\neq &0 \\ \\ p&-&2&\neq &0 \\ &+&2&&+2 \\ \hline &&p&\neq &2 \end{array}$
9. $10m\neq 0$
$m\neq 0$
10. $\phantom{a}$
$2(3x+10)\Rightarrow \begin{array}[t]{rrrrr} 3x&+&10&\neq &0 \\ &-&10&&-10 \\ \hline &&3x&\neq &-10 \\ \\ &&x&\neq &-\dfrac{10}{3} \end{array}$
11. $5(r+2)$
$r\neq -2$
12. $3n(2n+1)$
$\begin{array}[t]{rrr} n&\neq &0 \\ \\ n&\neq &-\dfrac{1}{2} \end{array}$
13. $(b-4)(b+8)$
$\begin{array}[t]{rrr} b&\neq &4 \\ b&\neq &-8 \end{array}$
14. $5v(7v-1)$
$\begin{array}[t]{rrr} v&\neq &0 \\ v&\neq &\dfrac{1}{7} \end{array}$
15. $\dfrac{21x^2}{18x}\Rightarrow \dfrac{\cancel{3}\cdot 7\cdot \cancel{x}\cdot x}{\cancel{3}\cdot 6\cdot \cancel{x}}\Rightarrow \dfrac{7x}{6}$
16. $\dfrac{12n}{4n^2}\Rightarrow \dfrac{3\cdot \cancel{4}\cdot \cancel{n}}{\cancel{4}\cdot \cancel{n}\cdot n}\Rightarrow \dfrac{3}{n}$
17. $\dfrac{24a}{40a^2}\Rightarrow \dfrac{3\cdot \cancel{8}\cdot \cancel{a}}{5\cdot \cancel{8}\cdot \cancel{a}\cdot a}\Rightarrow \dfrac{3}{5a}$
18. $\dfrac{21k}{24k^2}\Rightarrow \dfrac{\cancel{3}\cdot 7\cdot \cancel{k}}{\cancel{3}\cdot 8\cdot k}\Rightarrow \dfrac{7}{8k}$
19. $\dfrac{18m-24}{60}\Rightarrow \dfrac{\cancel{6}(3m-4)}{\cancel{6}(10)}\Rightarrow \dfrac{3m-4}{10}$
20. $\dfrac{n-9}{9n-81}\Rightarrow \dfrac{\cancel{n-9}}{9\cancel{(n-9)}}\Rightarrow \dfrac{1}{9}$
21. $\dfrac{x+1}{x^2+8x+7}\Rightarrow \dfrac{\cancel{x+1}}{\cancel{(x+1)}(x+7)}\Rightarrow \dfrac{1}{x+7}$
22. $\dfrac{28m+12}{36}\Rightarrow \dfrac{\cancel{4}(7m+3)}{\cancel{4}(9)}\Rightarrow \dfrac{7m+3}{9}$
23. $\dfrac{n^2+4n-12}{n^2-7n+10}\Rightarrow \dfrac{(n+6)\cancel{(n-2)}}{(n-5)\cancel{(n-2)}}\Rightarrow \dfrac{n+6}{n-5}$
24. $\dfrac{b^2+14b+48}{b^2+15b+56}\Rightarrow \dfrac{\cancel{(b+8)}(b+6)}{\cancel{(b+8)}(b+7)}\Rightarrow \dfrac{b+6}{b+7}$
25. $\dfrac{9v+54}{v^2-4v-60}\Rightarrow \dfrac{9\cancel{(v-6)}}{(v-10)\cancel{(v+6)}}\Rightarrow \dfrac{9}{v-10}$
26. $\dfrac{k^2-12k+32}{k^2-64}\Rightarrow \dfrac{\cancel{(k-8)}(k-4)}{\cancel{(k-8)}(k+8)}\Rightarrow \dfrac{k-4}{k+8}$
27. $\dfrac{2n^2+19n-10}{9n+90}\Rightarrow \dfrac{(2n-1)\cancel{(n+10)}}{9\cancel{(n+10)}}\Rightarrow \dfrac{2n-1}{9}$
28. $\dfrac{3x^2-29x+40}{5x^2-30x-80}\Rightarrow \dfrac{(3x-5)\cancel{(x-8)}}{5(x+2)\cancel{(x-8)}}\Rightarrow \dfrac{3x-5}{5(x+2)}$
29. $\dfrac{2x^2-10x+8}{3x^2-7x+4}\Rightarrow \dfrac{2(x-4)\cancel{(x-1)}}{(3x-4)\cancel{(x-1)}}\Rightarrow \dfrac{2(x-4)}{3x-4}$
30. $\dfrac{7n^2-32n+16}{4n-16}\Rightarrow \dfrac{(7n-4)\cancel{(n-4)}}{4\cancel{(n-4)}}\Rightarrow \dfrac{7n-4}{4}$
31. $\dfrac{7a^2-26a-45}{6a^2-34a+20}\Rightarrow \dfrac{\cancel{(a-5)}(7a+9)}{2(3a-2)\cancel{(a-5)}}\Rightarrow \dfrac{7a+9}{2(3a-2)}$
32. $\dfrac{4k^3-2k^2-2k}{k^3-18k^2+9k}\Rightarrow \dfrac{2k(2k^2-k-1)}{\cancel{k}(k^2-18k+9)}\Rightarrow \dfrac{2(2k^2-k-1)}{k^2-18k+9}$