\(A=\dfrac{7}{1.9}+\dfrac{7}{9.17}+\dfrac{7}{17.25}+...+\dfrac{7}{81.89}\)

\(\dfrac{8}{7}A=\dfrac{8}{1.9}+\dfrac{8}{9.17}+\dfrac{8}{17.25}+...+\dfrac{8}{81.89}\)

\(\dfrac{8}{7}A=1-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{25}+...+\dfrac{1}{81}-\dfrac{1}{89}\)

\(\dfrac{8}{7}A=1-\dfrac{1}{89}=\dfrac{88}{89}\Rightarrow A=\dfrac{88}{89}:\dfrac{8}{7}=\dfrac{77}{89}\)

\(B=\dfrac{5^2}{1.4}+\dfrac{3^2}{4.7}+\dfrac{3^2}{7.10}+...+\dfrac{3^2}{37.40}\)

\(B=\dfrac{25}{1.4}+\dfrac{9}{4.7}+\dfrac{9}{7.10}+...+\dfrac{9}{37.40}\)

\(\dfrac{1}{3}B=\dfrac{25}{12}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{37.40}\)

\(\dfrac{1}{3}B=\dfrac{25}{12}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{37}-\dfrac{1}{40}\)

\(\dfrac{1}{3}B=\dfrac{25}{12}+\dfrac{1}{4}-\dfrac{1}{40}=\dfrac{277}{120}\Rightarrow B=\dfrac{277}{120}:\dfrac{1}{3}=\dfrac{277}{40}\)

\(A=\dfrac{7}{1.9}+\dfrac{7}{9.17}+\dfrac{7}{17.25}+...+\dfrac{7}{81.89}\)

\(=7\left(\dfrac{8}{1.9}+\dfrac{8}{9.17}+\dfrac{8}{17.25}+...+\dfrac{8}{81.89}\right)\)

\(=7\left(1-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{25}+\dfrac{1}{25}+...+\dfrac{1}{81}-\dfrac{1}{89}\right)\)

\(=7.\left(1-\dfrac{1}{89}\right)=7.\dfrac{88}{89}=\dfrac{616}{89}\)

12-[800:[537-(2 mu 5+15 nhân 7]nhân 1 mu21

a) Ta có: \(\left(x+5\right)\left(x-4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+5=0\\x-4=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-5\\x=4\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}x=-5\\x=4\end{matrix}\right.\).

b) \(\left(3-x\right)\left(x-3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}3-x=0\\x-3=0\end{matrix}\right.\) \(\Rightarrow x=3\)

Vậy \(x=3\).

c) \(5\left(x+1\right)-3^2=3\left(2+x\right)-8\)

\(\Rightarrow5x+5-9=6+3x-8\)

\(\Rightarrow5x-3x=-5+9-8\)

\(\Rightarrow2x=-4\)

\(\Rightarrow x=-2\)

Vậy \(x=-2.\)

giúp mk câu này nha

x . ( x + 1 ) = 0

\(a,\dfrac{\left(-11\right).3+7.\left(-11\right)}{\left(-15\right).22}=\dfrac{\left(-11\right).\left(3+7\right)}{\left(-15\right).22}=\dfrac{-11.10}{-15.22}=\dfrac{-11.2.5}{-11.3.5+2.11}=\dfrac{-1}{-3}=\dfrac{1}{3}\\ \dfrac{25.11}{15.37-15.48}\\ =\dfrac{5.5.11}{15.\left(37-48\right)}=\dfrac{5.5.11}{15.\left(-11\right)}=\dfrac{5.5.11}{3.5.\left(-11\right)}=\dfrac{5}{-3}=-\dfrac{5}{3}\\ \dfrac{-2.3.5^2}{3^2.5^3}=\dfrac{-2}{3.5}=-\dfrac{2}{15}\)

Câu cuối là dấu âm ở giữa phân số nhé

3/3. (3/1.4 + 3/4.7 + 3/7.10 + .... + 3/67.70)=3/3. (1-1/4+1/4-1/7+1/7-1/10+ .... + 1/67-1/70)= 3/3. (1-1/70)=3/3. 69/70 = 207/210=69/70