4.2 Rational expressions: building rational expressions and the  (Page 4/4)

$\frac{4}{x^3},\frac{7}{x^5}$

$\frac{2x}{x+6},\frac{x}{x-1}$

$\frac{-3}{b^2-b},\frac{4b}{b^2-1}$

$\frac{8}{x^2-x-6},\frac{-1}{x^2+x-2}$

$\frac{10x}{x^2+8x+16},\frac{5x}{x^2-16}$

$\frac{-2a{b}^2}{a^3-6a^2},\frac{6b}{a^4-2a^3},\frac{-2a}{a^2-4a+4}$

$\frac{3}{x}=\frac{N}{x^3}$

$\frac{4}{a}=\frac{N}{a^2}$

$\frac{-2}{x}=\frac{N}{xy}$

$\frac{-7}{m}=\frac{N}{ms}$

$\frac{6a}{5}=\frac{N}{10b}$

$\frac{a}{3z}=\frac{N}{12z}$

$\frac{x^2}{4y^2}=\frac{N}{20y^4}$

$\frac{b^3}{6a}=\frac{N}{18a^5}$

$\frac{-4a}{5x^{2}y}=\frac{N}{15x^3{y}^3}$

$\frac{-10z}{7a^{3}b}=\frac{N}{21a^4{b}^5}$

$\frac{8x^{2}y}{5a^3}=\frac{N}{25a^3{x}^2}$

$\frac{2}{a^2}=\frac{N}{a^2\left(a-1\right)}$

$\frac{5}{x^3}=\frac{N}{x^3\left(x-2\right)}$

$\frac{2a}{b^2}=\frac{N}{b^3-b}$

$\frac{4x}{a}=\frac{N}{a^4-4a^2}$

$\frac{6b^3}{5a}=\frac{N}{10a^2-30a}$

$\frac{4x}{3b}=\frac{N}{3b^5-15b}$

$\frac{2m}{m-1}=\frac{N}{\left(m-1\right)\left(m+2\right)}$

$\frac{3s}{s+12}=\frac{N}{\left(s+12\right)\left(s-7\right)}$

$\frac{a+1}{a-3}=\frac{N}{\left(a-3\right)\left(a-4\right)}$

$\frac{a+2}{a-2}=\frac{N}{\left(a-2\right)\left(a-4\right)}$

$\frac{b+7}{b-6}=\frac{N}{\left(b-6\right)\left(b+6\right)}$

$\frac{5m}{2m+1}=\frac{N}{\left(2m+1\right)\left(m-2\right)}$

$\frac{4}{a+6}=\frac{N}{a^2+5a-6}$

$\frac{9}{b-2}=\frac{N}{b^2-6b+8}$

$\frac{3b}{b-3}=\frac{N}{b^2-11b+24}$

$\frac{-2x}{x-7}=\frac{N}{x^2-4x-21}$

$\frac{-6m}{m+6}=\frac{N}{m^2+10m+24}$

$\frac{4y}{y+1}=\frac{N}{y^2+9y+8}$

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

$\frac{y-3}{y+3}=\frac{N}{y^2-9}$

$\frac{a+5}{a-5}=\frac{N}{a^2-25}$

$\frac{z-4}{z+4}=\frac{N}{z^2-16}$

$\frac{4}{2a+1}=\frac{N}{2a^2-5a-3}$

$\frac{1}{3b-1}=\frac{N}{3b^2+11b-4}$

$\frac{a+2}{2a-1}=\frac{N}{2a^2+9a-5}$

$\frac{-3}{4x+3}=\frac{N}{4x^2-13x-12}$

$\frac{b+2}{3b-1}=\frac{N}{6b^2+7b-3}$

$\frac{x-1}{4x-5}=\frac{N}{12x^2-11x-5}$

$\frac{3}{x+2}=\frac{3x-21}{N}$

$\frac{4}{y+6}=\frac{4y+8}{N}$

$\frac{-6}{a-1}=\frac{-6a-18}{N}$

$\frac{-8a}{a+3}=\frac{-8a^2-40a}{N}$

$\frac{y+1}{y-8}=\frac{y^2-2y-3}{N}$

$\frac{x-4}{x+9}=\frac{x^2+x-20}{N}$

$\frac{3x}{2-x}=\frac{N}{x-2}$

$\frac{7a}{5-a}=\frac{N}{a-5}$

$\frac{-m+1}{3-m}=\frac{N}{m-3}$

$\frac{k+6}{10-k}=\frac{N}{k-10}$

$\frac{2}{a},\frac{3}{a^4}$

$\frac{5}{b^2},\frac{4}{b^3}$

$\frac{8}{z},\frac{3}{4z^3}$

$\frac{9}{x^2},\frac{1}{4x}$

$\frac{2}{a+3},\frac{4}{a+1}$

$\frac{2}{x+5},\frac{4}{x-5}$

$\frac{1}{x-7},\frac{4}{x-1}$

$\frac{10}{y+2},\frac{1}{y+8}$

$\frac{4}{a^2},\frac{a}{a+4}$

$\frac{-3}{b^2},\frac{b^2}{b+5}$

$\frac{-6}{b-1},\frac{5b}{4b}$

$\frac{10a}{a-6},\frac{2}{a^2-6a}$

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

$\frac{x+1}{x^2-x-6},\frac{x+4}{x^2+x-2}$

$\frac{x-5}{x^2-9x+20},\frac{4}{x^2-3x-10}$

$\frac{-4}{b^2+5b-6},\frac{b+6}{b^2-1}$

$\frac{b+2}{b^2+6b+8},\frac{b-1}{b^2+8b+12}$

$\frac{x+7}{x^2-2x-3},\frac{x+3}{x^2-6x-7}$

$\frac{2}{a^2+a},\frac{a+3}{a^2-1}$

$\frac{x-2}{x^2+7x+6},\frac{2x}{x^2+4x-12}$

$\frac{x-2}{2x^2+5x-3},\frac{x.-1}{5x^2+16x+3}$

$\frac{2}{x-5},\frac{-3}{5-x}$

$\frac{4}{a-6},\frac{-5}{6-a}$

$\frac{6}{2-x},\frac{5}{x-2}$

$\frac{k}{5-k},\frac{3k}{k-5}$

$\frac{2m}{m-8},\frac{7}{8-m}$

( [link] ) Factor $m^2{x}^3+m{x}^2+mx.$

( [link] ) Factor $y^2-10y+21.$

( [link] ) Write the equation of the line that passes through the points $\left(1,1\right)$ and $\left(4,-2\right)$ . Express the equation in slope-intercept form.

( [link] ) Reduce $\frac{y^2-y-6}{y-3}.$

( [link] ) Find the quotient: $\frac{x^2-6x+9}{x^2-x-6}÷\frac{x^2+2x-15}{x^2+2x}.$