8.1 Simplify rational expressions  (Page 2/5)

ⓐ $\frac{2x}{z}$
ⓑ $\frac{4p-1}{6p-5}$
ⓒ $\frac{n-3}{n^2+2n-8}$

ⓐ $\frac{10m}{11n}$
ⓑ $\frac{6y+13}{4y-9}$
ⓒ $\frac{b-8}{b^2-36}$

ⓐ $\frac{4x^{2}y}{3y}$
ⓑ $\frac{3x-2}{2x+1}$
ⓒ $\frac{u-1}{u^2-3u-28}$

ⓐ $\frac{5p{q}^2}{9q}$
ⓑ $\frac{7a-4}{3a+5}$
ⓒ $\frac{1}{x^2-4}$

$\frac{2x}{x-1}$

ⓐ $x=0$
ⓑ $x=2$
ⓒ $x=\mathrm{-1}$

$\frac{4y-1}{5y-3}$

ⓐ $y=0$
ⓑ $y=2$
ⓒ $y=\mathrm{-1}$

$\frac{2p+3}{p^2+1}$

ⓐ $p=0$
ⓑ $p=1$
ⓒ $p=\mathrm{-2}$

$\frac{x+3}{2-3x}$

ⓐ $x=0$
ⓑ $x=1$
ⓒ $x=\mathrm{-2}$

$\frac{y^2+5y+6}{y^2-1}$

ⓐ $y=0$
ⓑ $y=2$
ⓒ $y=\mathrm{-2}$

$\frac{z^2+3z-10}{z^2-1}$

ⓐ $z=0$
ⓑ $z=2$
ⓒ $z=\mathrm{-2}$

$\frac{a^2-4}{a^2+5a+4}$

ⓐ $a=0$
ⓑ $a=1$
ⓒ $a=\mathrm{-2}$

$\frac{b^2+2}{b^2-3b-4}$

ⓐ $b=0$
ⓑ $b=2$
ⓒ $b=\mathrm{-2}$

$\frac{x^2+3xy+2y^2}{2x^{3}y}$

1. ⓐ $x=1,y=\mathrm{-1}$
2. ⓑ $x=2,y=1$
3. ⓒ $x=\mathrm{-1},y=\mathrm{-2}$

$\frac{c^2+cd-2d^2}{c{d}^3}$

1. ⓐ $c=2,d=\mathrm{-1}$
2. ⓑ $c=1,d=\mathrm{-1}$
3. ⓒ $c=\mathrm{-1},d=2$

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

1. ⓐ $m=2,n=1$
2. ⓑ $m=\mathrm{-1},n=\mathrm{-1}$
3. ⓒ $m=3,n=2$

$\frac{2s^{2}t}{s^2-9t^2}$

1. ⓐ $s=4,t=1$
2. ⓑ $s=\mathrm{-1},t=\mathrm{-1}$
3. ⓒ $s=0,t=2$

$-\frac{4}{52}$

$-\frac{44}{55}$

$\frac{56}{63}$

$\frac{65}{104}$

$\frac{6a{b}^2}{12a^{2}b}$

$\frac{15xy}{3x^3{y}^3}$

$\frac{8m^{3}n}{12m{n}^2}$

$\frac{36v^3{w}^2}{27v{w}^3}$

$\frac{3a+6}{4a+8}$

$\frac{5b+5}{6b+6}$

$\frac{3c-9}{5c-15}$

$\frac{4d+8}{9d+18}$

$\frac{7m+63}{5m+45}$

$\frac{8n-96}{3n-36}$

$\frac{12p-240}{5p-100}$

$\frac{6q+210}{5q+175}$

$\frac{a^2-a-12}{a^2-8a+16}$

$\frac{x^2+4x-5}{x^2-2x+1}$

$\frac{y^2+3y-4}{y^2-6y+5}$

$\frac{v^2+8v+15}{v^2-v-12}$

$\frac{x^2-25}{x^2+2x-15}$

$\frac{a^2-4}{a^2+6a-16}$

$\frac{y^2-2y-3}{y^2-9}$

$\frac{b^2+9b+18}{b^2-36}$

$\frac{y^3+y^2+y+1}{y^2+2y+1}$

$\frac{p^3+3p^2+4p+12}{p^2+p-6}$

$\frac{x^3-2x^2-25x+50}{x^2-25}$

$\frac{q^3+3q^2-4q-12}{q^2-4}$

$\frac{3a^2+15a}{6a^2+6a-36}$

$\frac{8b^2-32b}{2b^2-6b-80}$

$\frac{\mathrm{-5}{c}^2-10c}{\mathrm{-10}{c}^2+30c+100}$

$\frac{4d^2-24d}{2d^2-4d-48}$

$\frac{3m^2+30m+75}{4m^2-100}$

$\frac{5n^2+30n+45}{2n^2-18}$

$\frac{5r^2+30r-35}{r^2-49}$

$\frac{3s^2+30s+24}{3s^2-48}$

$\frac{t^3-27}{t^2-9}$

$\frac{v^3-1}{v^2-1}$

$\frac{w^3+216}{w^2-36}$

$\frac{v^3+125}{v^2-25}$

$\frac{a-5}{5-a}$

$\frac{b-12}{12-b}$

$\frac{11-c}{c-11}$

$\frac{5-d}{d-5}$

$\frac{12-2x}{x^2-36}$

$\frac{20-5y}{y^2-16}$

$\frac{4v-32}{64-v^2}$

$\frac{7w-21}{9-w^2}$

$\frac{y^2-11y+24}{9-y^2}$

$\frac{z^2-9z+20}{16-z^2}$

$\frac{a^2-5z-36}{81-a^2}$

$\frac{b^2+b-42}{36-b^2}$

Tax Rates For the tax year 2015, the amount of tax owed by a single person earning between $37,450 and $90,750, can be found by evaluating the formula $0.25x-4206.25,$ where x is income. The average tax rate for this income can be found by evaluating the formula $\frac{0.25x-4206.25}{x}.$ What would be the average tax rate for a single person earning $50,000?

Work The length of time it takes for two people for perform the same task if they work together can be found by evaluating the formula $\frac{xy}{x+y}.$ If Tom can paint the den in $x=$ 45 minutes and his brother Bobby can paint it in $y=$ 60 minutes, how many minutes will it take them if they work together?

Explain how you find the values of x for which the rational expression $\frac{x^2-x-20}{x^2-4}$ is undefined.

Explain all the steps you take to simplify the rational expression $\frac{p^2+4p-21}{9-p^2}.$