\(A=\frac{9}{8}-\frac{8}{9}+\frac{3}{25}+\frac{1}{4}-\frac{5}{16}+\frac{19}{25}-\frac{1}{9}+\frac{2}{25}-\frac{1}{81}\)

\(A=\left(\frac{9}{8}+\frac{1}{4}-\frac{5}{16}\right)-\left(\frac{8}{9}+\frac{1}{9}-\frac{1}{81}\right)+\left(\frac{3}{25}+\frac{19}{25}+\frac{2}{25}\right)\)

\(A=\frac{17}{16}-\frac{80}{81}+\frac{24}{25}\)

\(A=\frac{33529}{32400}\)

A=1+2+3+...+99+100

a. \(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Leftrightarrow\left(x+1\right).\left(x+1\right)=8.2\)

\(\Leftrightarrow\left(x+1\right)^2=16\)

\(\Leftrightarrow\left(x+1\right)^2=2^4\)

\(\Leftrightarrow\left(x+1\right)=2^2\)

\(\Leftrightarrow\left(x+1\right)=4\)

\(\Leftrightarrow x=4-1=3\)

b. \(x:\left(9\frac{1}{2}-\frac{3}{2}\right)=\frac{0,4+\frac{2}{9}-\frac{2}{11}}{1,6+\frac{8}{9}-\frac{8}{11}}\)

\(\Leftrightarrow x:\left(\frac{10}{2}-\frac{3}{2}\right)=\frac{0,4+0,2-0,18}{1,6+0,8-0,72}\)

\(\Leftrightarrow x:\frac{7}{2}=\frac{\frac{21}{50}}{\frac{42}{25}}\)

\(\Leftrightarrow x=\frac{\frac{21}{50}}{\frac{42}{25}}.\frac{7}{2}\Leftrightarrow x=\frac{1}{4}.\frac{7}{2}=\frac{7}{8}\)

a )  \(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Rightarrow\left(x+1\right).\left(x+1\right)=2.8\)

\(\Rightarrow\left(x+1\right)^2=16\)

\(\Rightarrow\orbr{\begin{cases}x+1=4\\x+1=-4\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=4-1\\x=-4-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)

Dấu " \(\orbr{\begin{cases}\\\end{cases}}\)là hoặc nha !!! 

a)\(\frac{x+1}{2}=\frac{8}{x+1}\)

\(\Rightarrow\left(x+1\right)^2=8\times2=16\)

\(\Rightarrow\left(x+1\right)^2=4^2\)

\(\Rightarrow x+1=4\)

\(\Rightarrow x=4-1=3\)

b)tớ ko biết làm . ~ sorry~

~chuk bn hok giỏi~

\(\frac{A}{B}=\frac{\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+\frac{6}{4}+\frac{5}{5}+\frac{4}{6}+\frac{3}{7}+\frac{2}{8}+\frac{2}{9}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}}\)

\(\frac{A}{B}=\frac{\left(\frac{8}{2}+1\right)+\left(\frac{7}{3}+1\right)+...+\left(\frac{1}{9}+1\right)+1}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}}\)

\(\frac{A}{B}=\frac{\frac{10}{2}+\frac{10}{3}+\frac{10}{4}+...+\frac{10}{9}+\frac{10}{10}}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}}\)

\(\frac{A}{B}=\frac{10\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}}\)

\(\frac{A}{B}=10\)

\(A=\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+...+\frac{2}{8}+\frac{1}{9}\)

Tách 9=1+1+...+1 ( có 9 số 1)

\(\Rightarrow A=1+\left(\frac{8}{2}+1\right)+\left(\frac{7}{3}+1\right)+...+\left(\frac{2}{8}+1\right)+\left(\frac{1}{9}+1\right)\)

\(A=\frac{10}{10}+\frac{10}{2}+\frac{10}{3}+...+\frac{10}{8}+\frac{10}{9}\)

\(A=10.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)\)

\(\Rightarrow A:B=\frac{10.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)}{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}}=10\) ( vì \(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\ne0\) )

Vậy \(A:B=10\)

Bài 1:

\(A=\frac{\frac{1}{12}-\frac{2}{9}-1}{\frac{5}{18}+\frac{-3}{4}-\frac{1}{9}}\)

\(A=\frac{\frac{1}{12}-\frac{2}{9}-\frac{18}{18}}{\frac{5}{18}+\frac{9}{12}-\frac{1}{9}}\)

\(A=\frac{1}{3}-\frac{18}{5}\)\(A=\frac{5}{15}-\frac{54}{15}\)

\(A=\frac{-49}{15}\)

giúp với ạ

giải dc nhưng mà hoi lâu

a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)

\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)

\(x:\left(9\frac{1}{2}-\frac{3}{2}\right)=\frac{\frac{2}{9}+\frac{2}{5}-\frac{2}{11}}{\frac{8}{5}+\frac{8}{9}-\frac{8}{11}}\)

\(x:8=\frac{2\left(\frac{1}{9}+\frac{1}{5}-\frac{1}{11}\right)}{8\left(\frac{1}{5}+\frac{1}{9}-\frac{1}{11}\right)}\)

\(x:8=\frac{1}{4}\)

\(x=2\)

Vậy..........

\(\frac{7}{9}.\frac{3}{8}+\frac{7}{9}.\frac{5}{8}-\frac{1}{3}\)

\(=\frac{7}{9}.\left(\frac{3}{8}+\frac{5}{8}\right)-\frac{1}{3}\)

\(=\frac{7}{9}.1-\frac{1}{3}\)

\(=\frac{7}{9}-\frac{1}{3}\)

\(=\frac{4}{9}\)

7/9( 3/8+3/8) - 1/3 = 7/9.1-1/3 = 4/9

\(=\frac{7}{9}.\left(\frac{3}{8}+\frac{5}{8}\right)-\frac{1}{3}=\frac{7}{9}.1-\frac{1}{3}=\frac{7}{9}-\frac{3}{9}=\frac{4}{9}\)