Bài 1:
\(a,\dfrac{x}{15}+\dfrac{7}{20}=\dfrac{73}{60}\\ \dfrac{4x+7.3}{60}=\dfrac{73}{60}\\ 4x+21=73\\ 4x=73-21\\ 4x=52\\ x=\dfrac{52}{4}=13\\ Vậy:x=13\\ ---\\ b,\dfrac{9}{x}+\dfrac{-6}{35}=\dfrac{33}{70}\\ \dfrac{9}{x}=\dfrac{33}{70}+\dfrac{6}{35}=\dfrac{33+6.2}{70}\\ \dfrac{9}{x}=\dfrac{45}{70}=\dfrac{45:5}{70:5}=\dfrac{9}{14}\\ Vậy:x=14\)
Bài 2:
\(a,\dfrac{12}{13}=\dfrac{12.101}{13.101}=\dfrac{1212}{1313}\\ \dfrac{12}{13}=\dfrac{12.\left(-10101\right)}{13.\left(-10101\right)}=\dfrac{-121212}{-131313}\\ Vậy:\dfrac{12}{13}=\dfrac{1212}{1313}=\dfrac{-121212}{-131313}\left(ĐPCM\right)\\ ---\\ b,\dfrac{-22}{121}=\dfrac{-22:11}{121:11}=\dfrac{-2}{11}\\ Mà:\dfrac{-2}{11}=\dfrac{-2.\left(-2\right)}{11.\left(-2\right)}=\dfrac{4}{-22}\\ Và:\dfrac{-2}{11}=\dfrac{-2.5}{11.5}=\dfrac{-10}{55}\\ Vậy:\dfrac{-22}{121}=\dfrac{4}{-22}=-\dfrac{10}{55}\left(ĐPCM\right)\)
Bài 3:
\(a,-\dfrac{4}{10}+\dfrac{-3}{7}=\dfrac{-4.7-3.10}{70}=\dfrac{-28-30}{70}=\dfrac{-58}{70}\\ Và:-\dfrac{1}{2}=\dfrac{-35}{70}\\ Vì:\dfrac{-58}{70}< \dfrac{-35}{70}.Nên:-\dfrac{4}{10}+\dfrac{-3}{7}< \dfrac{-1}{2}\\ ---\\ b,-\dfrac{2}{3}-\dfrac{4}{5}=-\left(\dfrac{2}{3}+\dfrac{4}{5}\right)=-\left(\dfrac{2.5+4.3}{15}\right)=-\dfrac{22}{15}\\ Và:\dfrac{-5}{3}=\dfrac{-5.5}{3.5}=\dfrac{-25}{15}\\ Vì:\dfrac{-22}{15}>\dfrac{-25}{15}.Nên:-\dfrac{2}{3}-\dfrac{4}{5}>-\dfrac{5}{3}\\ ----\\c,-\dfrac{24}{16}+\dfrac{3}{12}=\dfrac{-3}{2}+\dfrac{1}{4}=\dfrac{-3.2+1}{4}=\dfrac{-5}{4}=\dfrac{-15}{12}\\ Và:\dfrac{-14}{12}-\dfrac{-3}{36}=\dfrac{3}{36}-\dfrac{14}{12}=\dfrac{1}{12}-\dfrac{14}{12}=-\dfrac{13}{12}\\ Vì:-\dfrac{15}{12}< -\dfrac{13}{12}.Nên:-\dfrac{24}{16}+\dfrac{3}{12}< \dfrac{-14}{12}-\dfrac{-3}{36}\)