8.2 Multiply and divide rational expressions

$\frac{12}{16}·\frac{4}{10}$

$\frac{32}{5}·\frac{16}{24}$

$\frac{18}{10}·\frac{4}{30}$

$\frac{21}{36}·\frac{45}{24}$

$\frac{5x^2{y}^4}{12x{y}^3}·\frac{6x^2}{20y^2}$

$\frac{8w^{3}y}{9y^2}·\frac{3y}{4w^4}$

$\frac{12a^{3}b}{b^2}·\frac{2a{b}^2}{9b^3}$

$\frac{4m{n}^2}{5n^3}·\frac{m{n}^3}{8m^2{n}^2}$

$\frac{5p^2}{p^2-5p-36}·\frac{p^2-16}{10p}$

$\frac{3q^2}{q^2+q-6}·\frac{q^2-9}{9q}$

$\frac{4r}{r^2-3r-10}·\frac{r^2-25}{8r^2}$

$\frac{s}{s^2-9s+14}·\frac{s^2-49}{7s^2}$

$\frac{x^2-7x}{x^2+6x+9}·\frac{x+3}{4x}$

$\frac{2y^2-10y}{y^2+10y+25}·\frac{y+5}{6y}$

$\frac{z^2+3z}{z^2-3z-4}·\frac{z-4}{z^2}$

$\frac{2a^2+8a}{a^2-9a+20}·\frac{a-5}{a^2}$

$\frac{28-4b}{3b-3}·\frac{b^2+8b-9}{b^2-49}$

$\frac{18c-2c^2}{6c+30}·\frac{c^2+7c+10}{c^2-81}$

$\frac{35d-7d^2}{d^2+7d}·\frac{d^2+12d+35}{d^2-25}$

$\frac{72m-12m^2}{8m+32}·\frac{m^2+10m+24}{m^2-36}$

$\frac{4n+20}{n^2+n-20}·\frac{n^2-16}{4n+16}$

$\frac{6p^2-6p}{p^2+7p-18}·\frac{p^2-81}{3p^2-27p}$

$\frac{q^2-2q}{q^2+6q-16}·\frac{q^2-64}{q^2-8q}$

$\frac{2r^2-2r}{r^2+4r-5}·\frac{r^2-25}{2r^2-10r}$

Probability The director of large company is interviewing applicants for two identical jobs. If $w=$ the number of women applicants and $m=$ the number of men applicants, then the probability that two women are selected for the jobs is $\frac{w}{w+m}·\frac{w-1}{w+m-1}.$

1. ⓐ Simplify the probability by multiplying the two rational expressions.
2. ⓑ Find the probability that two women are selected when $w=5$ and $m=10$ .

Area of a triangle The area of a triangle with base b and height h is $\frac{bh}{2}.$ If the triangle is stretched to make a new triangle with base and height three times as much as in the original triangle, the area is $\frac{9bh}{2}.$ Calculate how the area of the new triangle compares to the area of the original triangle by dividing $\frac{9bh}{2}$ by $\frac{bh}{2}$ .

1. ⓐ Multiply $\frac{7}{4}·\frac{9}{10}$ and explain all your steps.
2. ⓑ Multiply $\frac{n}{n-3}·\frac{9}{n+3}$ and explain all your steps.
3. ⓒ Evaluate your answer to part (b) when $n=7.$ Did you get the same answer you got in part (a)? Why or why not?

1. ⓐ Divide $\frac{24}{5}÷6$ and explain all your steps.
2. ⓑ Divide $\frac{x^2-1}{x}÷(x+1)$ and explain all your steps.
3. ⓒ Evaluate your answer to part (b) when $x=5.$ Did you get the same answer you got in part (a)? Why or why not?