mn làm dùm mk nha

\(\frac{5}{11}.\frac{4}{9}+\frac{5}{11}.\frac{8}{9}-\frac{5}{11}.\frac{1}{9}\)

\(=\frac{5}{11}\left(\frac{4}{9}+\frac{8}{9}-\frac{1}{9}\right)\)

\(=\frac{5}{11}.\frac{11}{9}=\frac{5}{9}\)

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a, \(3x-4=6+2x\)

\(\Leftrightarrow3x-4-6-2x=0\)

\(\Leftrightarrow x-10=0\Leftrightarrow x=10\)

b, \(\frac{27}{40}x-\frac{3}{\frac{4}{15}}=\frac{2}{\frac{1}{12}}\)

\(\Leftrightarrow\frac{27}{40}x-\frac{45}{4}=24\Leftrightarrow\frac{27}{40}x=\frac{141}{4}\Leftrightarrow x=\frac{470}{9}\)

Ta có : \(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2019}\)

\(=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2019}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2018}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}+\frac{1}{2019}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{2018}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2019}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1009}\right)\)

\(=\frac{1}{1010}+\frac{1}{1011}+\frac{1}{1012}+...+\frac{1}{2019}=B\)

\(\Rightarrow A-B-1=-1\)

\(\Rightarrow\left(A-B-1\right)^{2019}=-1\)

(x + 1)(3 - x) > 0

th1 : x + 1 > 0 và  3 - x > 0

=> x > -1 và x < 3

=> -1 < x < 3

th2 : 

x + 1 < 0 và 3 - x < 0

=> x < -1 và x > 3

=> vô lí

\(\left(x+1\right)\left(-x+3\right)\ge0\)

\(th1\orbr{\begin{cases}x+1=0\\-x+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\-x=-3\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=3\end{cases}\left(1\right)}\)

 \(\left(x+1\right)\left(-x+3\right)>0\)=> x+1 và -x+3 cùng dấu

\(th2\orbr{\begin{cases}x+1>0\\-x+3>0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x>-1\\x< 3\end{cases}}\Leftrightarrow-1< x< 3\left(2\right)\)

\(th3\orbr{\begin{cases}x+1< 0\\-x+3< 0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x< -1\\x>3\end{cases}}\Leftrightarrow3< x< -1\left(ktm\right)\)

từ 1 và 2 \(\Rightarrow-1\le x\le3\)

vậy với\(-1\le x\le3\)thì\(\left(x+1\right)\left(-x+3\right)\ge0\)

\(\frac{-7}{25}\times\frac{39}{-14}\times\frac{50}{78}\)

\(=\frac{39}{50}\times\frac{50}{78}\)

\(=\frac{1}{2}\)

\(\frac{-7}{25}\)x \(\frac{39}{-14}\)x \(\frac{50}{78}\)

= \(\frac{-7}{25}\)x \(\frac{-14}{39}\)x \(\frac{25}{39}\)

=\(\frac{-7}{25}\)x\(\frac{25}{39}\)x \(\frac{-14}{39}\)

=\(\frac{-7}{39}\)x \(\frac{-14}{39}\)

=\(\frac{98}{1521}\)

chúc bạn học tốt !!!