Chapter 8

ⓐ $x=0$ ⓑ $n=-\frac{1}{3}$ ⓒ $a=\mathrm{-1},a=\mathrm{-3}$

ⓐ $q=0$ ⓑ $y=-\frac{2}{3}$ ⓒ $m=2,m=\mathrm{-3}$

ⓐ $\mathrm{-2}$ ⓑ $\frac{2}{9}$ ⓒ $-\frac{1}{3}$

ⓐ $\frac{4}{3}$ ⓑ $6$ ⓒ $\mathrm{-1}$

ⓐ $\frac{1}{2}$ ⓑ $\frac{1}{3}$ ⓒ 2

ⓐ $\frac{2}{3}$ ⓑ $\frac{4}{5}$ ⓒ $\frac{1}{2}$

ⓐ $\mathrm{-4}$ ⓑ $0$ ⓒ $\frac{4}{9}$

ⓐ $0$ ⓑ $\frac{3}{16}$ ⓒ $\frac{3}{16}$

$-\frac{5}{9}.$

$-\frac{7}{9}$

$\frac{x}{3y}$

$\frac{8x}{y}$

$\frac{3}{2}$

$\frac{7}{5}$

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

$\frac{x-5}{x-1}$

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

$\frac{x+1}{x-7}$

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

$\frac{p^2+2}{p+5}$

$\frac{n}{2\left(n+1\right)}$

$\frac{x}{2\left(x+2\right)}$

$\frac{2\left(x-3\right)}{3\left(x+3\right)}$

$\frac{5\left(x-1\right)}{2\left(x+5\right)}$

$\frac{p^2+4p+16}{p+4}$

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

$\mathrm{-1}$

$\mathrm{-1}$

$-\frac{2}{y+5}.$

$-\frac{3}{9+y}$

$-\frac{x+1}{x+5}$

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

$\frac{3}{4}$

$1$

$\frac{5p^2}{2q}$

$\frac{12y^3}{7}$

$\frac{x-2}{2\left(x+3\right)}$

$\frac{3(x-6)}{x+5}$

$\frac{x+5}{x}$

$\frac{x-4}{x+3}$

$-\frac{6(x+3)}{x+2}$

$-\frac{v}{3}$

$1$

1

$-\frac{1}{c-3}$

$-\frac{1}{2+d}$

$\frac{(m-2)}{4(m-8)}$

$\frac{n(n-2)}{n-1}$

$\frac{(a-3)(a+5)}{(a-5)(a-5)}$

$-\frac{(b+2)(b-1)}{(1+b)(b+4)}$

$\frac{2\left(x^2+2x+4\right)}{\left(x+2\right)\left(x^2-2x+4\right)}$

$\frac{2z(z^2+z+1)}{(z+1)(z^2-z+1)}$

$\frac{x-8}{2(x+1)}$

$\frac{y-2}{3y(y-4)}$

$\frac{x+2}{4}$

$\frac{2}{y+5}$

$\frac{2(m+1)(m+2)}{3(m+4)(m-3)}$

$\frac{(n+5)(n+9)}{2(n+6)(2n+3)}$

$\frac{3}{4}$

$\frac{2}{5}$

$\frac{5x+2}{2x+3}.$

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

$x+2$

$x+3$

$x-3$

$2x+5$

$n+3$

$y-8$

$\frac{x-11}{x-2}$

$\frac{x-3}{x+9}$

$3$

$y+3$

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

$\frac{3n-2}{n-1}$

$(x-4)(x+4)(x+3)$

$(x+3)(x+6)(x+5)$

$\frac{2x+8}{(x-4)(x+3)(x+4)},$
$\frac{x+3}{(x-4)(x+3)(x+4)}$

$\frac{x^2+6x}{(x+3)(x+5)(x+6)},$
$\frac{x+3}{(x+3)(x+5)(x+6)}$

$\frac{19}{20}$

$\frac{33}{40}$

$\frac{4b+25a}{30a^2{b}^2}$

$\frac{5d^2+6}{16c{d}^2}$

$\frac{7x-4}{(x+3)(x-2)}$

$\frac{7m+25}{(m+3)(m+4)}$

$\frac{x(5x+7y)}{y(x-y)(x+y)}$

$\frac{7m+15}{2(m+3)(m+1)}$

$\frac{5m^2-9m+2}{(m-2)(m+1)(m+2)}$

$\frac{2(n^2+6n-15)}{(n+2)(n-5)(n+3)}$

$\frac{\mathrm{-7}y+8}{(y+4)(y-5)}$

$\frac{4z+9}{(z+2)(z+3)}$

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

$\frac{\mathrm{-3}}{z-3}$

$\frac{1}{x-6}$

$\frac{y+3}{y+4}$

$\frac{\text{−}x+22}{x-7}$

$\frac{\mathrm{-2}(3y-4)}{2y-1}$

$\frac{v+3}{v+1}$

$\frac{3w}{w+7}$

$\frac{2}{3(x-1)}$

$\frac{1}{2(x-3)}$

$\frac{14}{11}$

$\frac{10}{23}$

$\frac{y+x}{y-x}$

$\frac{ab}{b-a}$

$b(b+2)$

$\frac{3}{c+3}$

$\frac{7}{3}$

$\frac{7}{3}$

$\frac{b+a}{a^2+b^2}$

$\frac{y-x}{xy}$

$\frac{3x-6}{5x+7}$

$\frac{x+21}{6x+43}$

$\frac{3}{5x+22}$

$\frac{6y+34}{3y}$

$\frac{x}{x+4}$

$\frac{x(x+1)}{3(x-1)}$

$-\frac{15}{7}$

$\frac{15}{13}$

$5,\mathrm{-3}$

$6,\mathrm{-2}$

$\mathrm{-2}$

$\mathrm{-2}$

$\frac{2}{3}$

$2$

$\mathrm{-1},\mathrm{-2}$

$\mathrm{-2},\mathrm{-3}$

no solution

no solution

$\mathrm{-2}$

$\mathrm{-3}$

$\mathrm{-4},3$

$7$

no solution

no solution

$L=\frac{A}{W}$

$A=\frac{F}{M}$

$x=\frac{3y-8}{2}$

$y=\frac{x}{1+x}$

$a=\frac{b}{cb-1}$

$y=\frac{3x}{6+x}$

$77$

$104$

$65$

$24$

$33$

$14$

$42$

$6$

$12\text{ml}$

$180\text{ml}$

$464\text{calories}$

$5\text{pieces}$

$590.4\text{Euros}$

$\mathrm{56,460}\text{yen}$

8

22.5

150 miles

350 miles

40 feet

60 feet

15 mph

$\text{17 mph}$

$\text{10 mph}$

$\text{50 mph}$

$\text{15 mph}$

$\text{6 mph}$

$2\text{hours and 24 minutes}$

$2\text{hours and 6 minutes}$

16.25 hours

12 hours

$y=\frac{3}{10}x$

$y=3x$

ⓐ $c=4.8t$ ⓑ 432 calories

ⓐ $d=50t$ ⓑ 250 miles

ⓐ $m=55h$ ⓑ 220 miles

ⓐ $w=6v$ ⓑ 78 pounds

ⓐ $d=16t^2$ ⓑ 256 feet

ⓐ $A=3.14r^2$ ⓑ 254.34 square inches

$p=\frac{360}{q}$

$y=\frac{16}{x}$

ⓐ $t=\frac{1000}{r}$ ⓑ 2 hours

ⓐ $h=\frac{130}{t}$ ⓑ $1\frac{2}{3}$ hours

ⓐ $F=\frac{48}{L}$ ⓑ 9.6 pounds

ⓐ $z=0$ ⓑ $p=\frac{5}{6}$
ⓒ $n=\mathrm{-4},n=2$

ⓐ $y=0$ ⓑ $x=-\frac{1}{2}$
ⓒ $u=\mathrm{-4},u=7$

ⓐ $0$ ⓑ $4$ ⓒ $1$

ⓐ $3$ ⓑ $\frac{5}{2}$ ⓒ $-\frac{1}{5}$

ⓐ $\mathrm{-6}$ ⓑ $\frac{20}{3}$ ⓒ $0$

ⓐ $\mathrm{-1}$ ⓑ $-\frac{3}{10}$ ⓒ $0$

ⓐ $0$ ⓑ $\frac{3}{4}$ ⓒ $\frac{15}{4}$

ⓐ $0$ ⓑ $-\frac{3}{5}$ ⓒ $-\frac{7}{20}$

$-\frac{1}{13}$

$\frac{8}{9}$

$\frac{b}{2a}$

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

$\frac{3}{4}$

$\frac{3}{5}$

$\frac{7}{5}$

$\frac{12}{5}$

$\frac{a+3}{a-4}$

$\frac{y+4}{y-5}$

$\frac{x-5}{x-3}$

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

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

$x-2$

$\frac{a(a+5)}{2(a+3)(a-2)}$

$\frac{c}{2(c-5)}$

$\frac{3(m+5)}{4(m-5)}$

$\frac{5(r-1)}{r+7}$

$\frac{t^2+3t+9}{t+3}$

$\frac{w^2-6w+36}{w-6}$

$\mathrm{-1}$

$\mathrm{-1}$

$-\frac{2}{x+6}$

$-\frac{4}{8+v}$

$(-\frac{y-8)}{3+y}$

$-\frac{a+4}{9+a}$

16.5%

Answers will vary, but all should reference setting the denominator function to zero.

$\frac{3}{10}$

$\frac{6}{25}$

$\frac{x^3}{8y}$

$\frac{8a^3}{3b^2}$

$\frac{p(p-4)}{2(p-9)}$

$\frac{r+5}{2r(r+2)}$

$\frac{x-7}{4(x+3)}$

$\frac{z+3}{z(z+1)}$

$-\frac{4(b+9)}{3(b+7)}$

$\mathrm{-7}$

$1$

$1$

$-\frac{2t}{t^3-5t-9}$

$-\frac{1}{10-w}$

$\frac{3y^2(y+6)(y+7)}{(y-7)(y^2+6)}$

$\frac{a(a-5)}{a-6}$

$\frac{(c+2)(c+2)}{(c-2)(c-3)}$

$-\frac{(m-2)(m-3)}{(3+m)(m+4)}$

$\frac{3s}{s+4}$

$\frac{4(p^2-pq+q^2)}{(p-q)(p^2+pq+q^2)}$

$\frac{t+3}{2t(t-3)}$

$\frac{y+3z}{2y(2y-1)}$

$\frac{2a-7}{5}$

$3\left(3c-5\right)$

$\frac{4(m+8)(m+7)}{3(m-4)(m+2)}$

$\frac{(4p+1)(p-7)}{3p(p+9)(p-1)}$

ⓐ $\frac{w\left(w-1\right)}{\left(w+m\right)\left(w+m-1\right)}$
ⓑ $\frac{2}{21}$

Answers will vary.

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{3a+1}{a–b}$

$\frac{d+5}{d+8}$

$p+8$

$r+8$

$8t$

$\frac{2w}{w-4}$

$y-8$

$3a+7$

$c+2$

$\frac{m-2}{3}$

$\frac{p+3}{p+5}$

$\frac{r+9}{r+7}$

$4$

$x+2$

$\frac{z+4}{z-5}$

$\frac{4b-3}{b-7}$

$\frac{32r+32}{r\left(r+4\right)}$

$(x-4)(x+2)(x+3)$

$(z-2)(z+4)(z+2)$

$(b+3)(b+3)(b-5)$

$(3d-1)(d+5)(d-6)$

$\frac{5x+15}{(x-4)(x+2)(x+3)},$
$\frac{2x^2+4x}{(x-4)(x+2)(x+3)}$