\(\Leftrightarrow-\dfrac{16}{279}< \dfrac{x}{9}< =\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{x}{9}=0\)

hay x=0

\(a,\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right).\)

\(=\left(\dfrac{21}{60}+\dfrac{44}{60}-\dfrac{75}{60}\right):\left(\dfrac{99}{180}-\dfrac{104}{180}\right).\)

\(=\left(\dfrac{65}{60}-\dfrac{75}{60}\right):\left(-\dfrac{5}{180}\right).\)

\(=-\dfrac{10}{60}:\left(-\dfrac{5}{180}\right).\)

\(=-\dfrac{1}{6}:\left(-\dfrac{1}{36}\right).\)

\(=-\dfrac{1}{6}.\left(-36\right).\)

\(=\dfrac{-1.\left(-36\right)}{6}=\dfrac{36}{6}=6.\)

Vậy......

\(b,\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}.\)

\(=\dfrac{5\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}{8\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}.\)

\(=\dfrac{5}{8}:\dfrac{15}{16}.\)

\(=\dfrac{5}{8}.\dfrac{16}{15}=\dfrac{5.16}{8.15}=\dfrac{1.2}{1.3}=\dfrac{2}{3}.\)

Vậy......

c, (làm tương tự câu b).

~ Học tốt!!! ~

\(\dfrac{3}{12}+\dfrac{1}{4}=\dfrac{3:3}{12:3}+\dfrac{1}{4}=\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{2}{4}=\dfrac{1}{2}\)

\(\dfrac{4}{10}+\dfrac{3}{5}=\dfrac{4:2}{10:2}+\dfrac{3}{5}=\dfrac{2}{5}+\dfrac{3}{5}=\dfrac{5}{5}=1\)

\(\dfrac{12}{27}+\dfrac{2}{9}=\dfrac{12:3}{27:3}+\dfrac{2}{9}=\dfrac{4}{9}+\dfrac{2}{9}=\dfrac{6}{9}=\dfrac{2}{3}\)

\(\dfrac{7}{3}+\dfrac{20}{15}=\dfrac{7}{3}+\dfrac{20:5}{15:5}=\dfrac{7}{3}+\dfrac{4}{3}=\dfrac{11}{3}\)

a: Ta có: \(\dfrac{8}{9}-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\right)\)

\(=\dfrac{8}{9}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{3}-...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)

=0

B= \(\dfrac{3}{2}-\dfrac{5}{6}+\dfrac{7}{12}-\dfrac{9}{20}+\dfrac{11}{30}-\dfrac{13}{42}+\dfrac{15}{56}\)

= \(\left(1+\dfrac{1}{2}\right)-\left(\dfrac{1}{2}+\dfrac{1}{3}\right)+\left(\dfrac{1}{3}+\dfrac{1}{4}\right)-\left(\dfrac{1}{4}+\dfrac{1}{5}\right)+\left(\dfrac{1}{5}+\dfrac{1}{6}\right)-\left(\dfrac{1}{6}+\dfrac{1}{7}\right)+\left(\dfrac{1}{7}+\dfrac{1}{8}\right)\)

= 1+\(\dfrac{1}{8}\)=\(\dfrac{9}{8}\)

\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\\ \Leftrightarrow \frac{x-9}{15}=\frac{y-12}{20}=\frac{z-24}{40}\\ \Leftrightarrow \frac{x}{15}-\frac{3}{5}=\frac{y}{20}-\frac{3}{5}=\frac{z}{40}-\frac{3}{5}\\ \Leftrightarrow \frac{x}{15}=\frac{y}{20}=\frac{z}{40}\\\frac{x}{15}=\frac{y}{20}=\frac{z}{40}=k\\ \Rightarrow x=15k;y=20k;z=40k\\ xy=1200\\ \Leftrightarrow 15k.20k=300k^2=1200\\ \Leftrightarrow k^2=4\)

\(\Rightarrow\left[{}\begin{matrix}k=2\\k=-2\end{matrix}\right.\\ k=2\Rightarrow\left\{{}\begin{matrix}x=15k=15.2=30\\y=20k=20.2=40\\z=40k=40.2=80\end{matrix}\right.\\ k=-2\Rightarrow\left\{{}\begin{matrix}x=15k=15.\left(-2\right)=-30\\y=20k=20.\left(-2\right)=-40\\z=40k=40.\left(-2\right)=-80\end{matrix}\right.\)

\(\dfrac{15}{x-9}=\dfrac{20}{y-12}=\dfrac{40}{z-24}\)

\(\Rightarrow\dfrac{x-9}{15}=\dfrac{y-12}{20}=\dfrac{z-24}{40}=k\)

\(\Rightarrow\left(15k+9\right)\left(20k+12\right)=1200\)

\(\Rightarrow3.4\left(5k+3\right)\left(5k+3\right)=1200\)

\(\Rightarrow\left(5k+3\right)\left(5k+3\right)=1200:3:4\)

\(\Rightarrow\left(5k+3\right)^2=100\)

\(\Rightarrow\left[{}\begin{matrix}5k+3=10\\5k+3=-10\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}k=\dfrac{7}{5}\\k=\dfrac{-13}{5}\end{matrix}\right.\)

+) Với \(k=\dfrac{7}{5}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7}{5}.15+9\\y=\dfrac{7}{5}.20+12\\z=\dfrac{7}{5}.40+24\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=30\\y=40\\z=80\end{matrix}\right.\)

+) Với \(k=\dfrac{-13}{5}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-13}{5}.15+9\\y=\dfrac{-13}{5}.20+12\\z=\dfrac{-13}{5}.40+24\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-30\\y=-40\\z=-80\end{matrix}\right.\)

Vậy .................

-2/15

-4/35

-5/3

10

-8/3

-7/2

-9

-4/3

Chúc em học giỏi

\(=\dfrac{-2}{15}\\ =\dfrac{-4}{35}\\ =-1\\ =10\\ =\dfrac{-8}{3}\\ =-7\\ =-9\\ =\dfrac{-4}{3}\)

-2/15

-4/35

-5/3

10

-8/3

-7/2

-9

-4/3