(11) Max. and min. for ${\displaystyle x=7.5}$, ${\displaystyle y=\pm 5.414}$. (See example no. 10, here.)

(12) Min.: ${\displaystyle x={\tfrac {1}{2}}}$, ${\displaystyle y=0.25}$; max.: ${\displaystyle x=-{\tfrac {1}{3}}}$, ${\displaystyle y=1.408}$.

(1) ${\displaystyle {\dfrac {2}{x-3}}+{\dfrac {1}{x+4}}}$.

(2) ${\displaystyle {\dfrac {1}{x-1}}+{\dfrac {2}{x-2}}}$.

(3) ${\displaystyle {\dfrac {2}{x-3}}+{\dfrac {1}{x+4}}}$.

(4) ${\displaystyle {\dfrac {5}{x-4}}-{\dfrac {4}{x-3}}}$.

(5) ${\displaystyle {\dfrac {19}{13(2x+3)}}-{\dfrac {22}{13(3x-2)}}}$.

(6) ${\displaystyle {\dfrac {2}{x-2}}+{\dfrac {4}{x-3}}-{\dfrac {5}{x-4}}}$.

(7) ${\displaystyle {\dfrac {1}{6(x-1)}}+{\dfrac {11}{15(x+2)}}+{\dfrac {1}{10(x-3)}}}$.

(8) ${\displaystyle {\dfrac {7}{9(3x+1)}}+{\dfrac {71}{63(3x-2)}}-{\dfrac {5}{7(2x+1)}}}$.

(9) ${\displaystyle {\dfrac {1}{3(x-1)}}+{\dfrac {2x+1}{3(x^{2}+x+1)}}}$.

(10) ${\displaystyle x+{\dfrac {2}{3(x+1)}}+{\dfrac {1-2x}{3(x^{2}-x+1)}}}$.

(11) ${\displaystyle {\dfrac {3}{(x+1)}}+{\dfrac {2x+1}{x^{2}+x+1}}}$.

(12) ${\displaystyle {\dfrac {1}{x-1}}-{\dfrac {1}{x-2}}+{\dfrac {2}{(x-2)^{2}}}}$.

(13) ${\displaystyle {\dfrac {1}{4(x-1)}}-{\dfrac {1}{4(x+1)}}+{\dfrac {1}{2(x+1)^{2}}}}$.

(14) ${\displaystyle {\dfrac {4}{9(x-1)}}-{\dfrac {4}{9(x+2)}}-{\dfrac {1}{3(x+2)^{2}}}}$.

(15) ${\displaystyle {\dfrac {1}{x+2}}-{\dfrac {x-1}{x^{2}+x+1}}-{\dfrac {1}{(x^{2}+x+1)^{2}}}}$.

(16) ${\displaystyle {\dfrac {5}{x+4}}-{\dfrac {32}{(x+4)^{2}}}+{\dfrac {36}{(x+4)^{3}}}}$.

(17) ${\displaystyle {\dfrac {7}{9(3x-2)^{2}}}+{\dfrac {55}{9(3x-2)^{3}}}+{\dfrac {73}{9(3x-2)^{4}}}}$.

(18) ${\displaystyle {\dfrac {1}{6(x-2)}}+{\dfrac {1}{3(x-2)^{2}}}-{\dfrac {x}{6(x^{2}+2x+4)}}}$.