Answer Key 8.1

  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. \begin{array}{rrrrr} \\ \\ k&+&10&\neq &0 \\ &-&10&&-10 \\ \midrule &&k&\neq &-10 \end{array}
  8. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ \\ &&18p(p&-&2) \\ \\ &&18p&\neq &0 \\ &&p&\neq &0 \\ \\ p&-&2&\neq &0 \\ &+&2&&+2 \\ \midrule &&p&\neq &2 \end{array}
  9. \begin{array}{rrr} \\ 10m&\neq& 0 \\ m& \neq &0 \end{array}
  10. 2(3x+10)\Rightarrow \begin{array}{rrrrr} \\ \\ \\ \\ \\ 3x&+&10&\neq &0 \\ &-&10&&-10 \\ \midrule &&3x&\neq &-10 \\ \\ &&x&\neq &-\dfrac{10}{3} \end{array}
  11. \begin{array}{rrr} \\ 5(r&+&2) \\ r& \neq & -2 \end{array}
  12. \begin{array}{rrr} \\ \\ \\ \\ 3n(2n&+&1) \\ n&\neq &0 \\ \\ n&\neq &-\dfrac{1}{2} \end{array}
  13. \begin{array}{rrr} \\ \\ (b-4)(b+8)&& \\ b&\neq &4 \\ b&\neq &-8 \end{array}
  14. \begin{array}{rrr} \\ \\ \\ 5v(7v&-&1) \\ 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}

License

Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

Share This Book