Answer key

1. (a). $\dfrac{2}{9}$

   (b). Undefined.

2. (a). $x=3, -3$

   (b). $x=-1, 8$

3. (a). $\dfrac{7x+2}{x+1}$

   (b). $\dfrac{x+3}{x-3}$

4. (a). $\dfrac{9}{x-1}$

   (b). $\dfrac{x+1}{7}$

5. (a). $\dfrac{(2x-9)(x+5)}{(x-7)(x-1)}$

   (b). $\dfrac{5x+8}{x(x+2)}$

6. (a). $\dfrac{u-6}{u-7}$

   (b). $\dfrac{x+8}{x-6}$

7. (a). $n=\dfrac{9mp}{m-5p}$

   (b). $\dfrac{2v}{vy-7}$

8. (a). $x=8, -2$

   (b). $x=4, 3$

9. (a). $52$ men

   (b). $36$ orange marbles

10. (a). $22.8$ minutes

    (b). $14$ minutes

11. (a). 5 kilometers/hour.

    (b). 55 miles/hour.

12. (a). $x^8$

    (b). $|u^{11}|$

13. (a). $[0, \infty)$

    (b). $[-15, \infty)$

14. (a). $\dfrac{1}{b^{\dfrac{5}{12}}}$

    (b). $z^\dfrac{4}{3}$

15. (a). $5x^4y^2\sqrt{2xy}$

    (b). $2yz^3\sqrt{6z}$

16. (a). $2xz^4\sqrt[3]{9z^2}$

    (b). $2xw^3\sqrt[5]{5x^3}$

    (c). $2x^4w\sqrt[4]{6w^2}$

17. (a). $19y^2\sqrt{5y}$

    (b). $2w^3\sqrt{w}$

18. (a). $10\sqrt{6}+10\sqrt{15}-2-\sqrt{10}$

    (b). $80+27\sqrt{30}$

19. (a). $\sqrt[15]{y^{14}}$

    (b). $\sqrt[3]{x}$

20. (a). $\dfrac{-18\sqrt{u}-9}{8u-2}$

    (b). $\dfrac{35-14\sqrt{w}}{25-4w}$

21. (a). ${\dfrac{\sqrt[4]{40}}{2}}$

    (b). ${\dfrac{\sqrt[3]{12}}{4}}$

22. (a). $u=3$

    (b). $w=5, 4$

23. (a). $-7+8i$

    (b). $-1+4i$

24. (a). $3-9i$

    (b). $8-34i$

25. (a). $\dfrac{2}{13}-\dfrac{7}{26}i$

    (b). $i$

26. (a). $-i$

    (b). $-1$