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1)
A = \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+..+\frac{2}{99.101}\)
A = \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+..+\frac{1}{99}-\frac{1}{101}\)
A = \(\frac{1}{1}-\frac{1}{101}\)
A = \(\frac{100}{101}\)
Vậy A = \(\frac{100}{101}\)
B = \(\frac{5}{1.3}+\frac{5}{3.5}+...+\frac{5}{99.101}\)
B = \(\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)
B = \(\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)
B = \(\frac{5}{2}\left(\frac{1}{1}-\frac{1}{101}\right)\)
B = \(\frac{5}{2}.\frac{100}{101}\)
B = \(\frac{250}{101}\)
Vậy B = \(\frac{250}{101}\)
2)
Gọi ƯCLN ( 2n + 1 ; 3n + 2 ) = d ( d \(\in\)N* )
\(\Rightarrow\hept{\begin{cases}2n+1⋮d\\3n+2⋮d\end{cases}\Rightarrow\hept{\begin{cases}3\left(2n+1\right)⋮d\\2\left(3n+2\right)⋮d\end{cases}}}\)
\(\Rightarrow\hept{\begin{cases}6n+3⋮d\\6n+4⋮d\end{cases}\Rightarrow\left(6n+4\right)-\left(6n+3\right)⋮d\Rightarrow1⋮d}\)
\(\Rightarrow d=1\)
Vậy \(\frac{2n+1}{3n+2}\)là p/s tối giản
Gọi ƯCLN ( 2n+3 ; 4n+4 ) = d ( d \(\in\)N* )
\(\Rightarrow\hept{\begin{cases}2n+3⋮d\\4n+4⋮d\end{cases}\Rightarrow\hept{\begin{cases}2n+3⋮d\\\left(4n+4\right):2⋮d\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}2n+3⋮d\\2n+2⋮d\end{cases}\Rightarrow\left(2n+3\right)-\left(2n+2\right)⋮d}\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
Vậy ...
a,ĐK : x \(\ne\)3/7
\(\frac{24}{7x-3}=-\frac{4}{25}\Leftrightarrow600=-28x+12\Leftrightarrow-28x=588\Leftrightarrow x=-21\)
b, ĐK : x;y \(\ne\)6
Xét : \(\frac{4}{x-6}=-\frac{12}{18}\Leftrightarrow72=-12x+72\Leftrightarrow x=0\)
Xét : \(\frac{y}{24}=-\frac{12}{18}\Leftrightarrow18y=-288\Leftrightarrow y=-16\)
\(\frac{24}{7.x-3}=-\frac{4}{25}\)
24.25=7.x-3.-4
600=7.x-3.-4
7.x-3.-4=600
7.x-3=600:-4
7.x-3=-150
7.x=-150+3
7.x=-147
x=-147:7
x=-21
vậy x=-21
Ta có:
a) \(\Leftrightarrow3\left(x+2\right)=-4\left(x-5\right)\)
\(\Leftrightarrow3x+6=-4x+20\)
\(\Leftrightarrow7x=14\Leftrightarrow x=2\)
\(\frac{1}{3}+\frac{-2}{5}+\frac{1}{6}-\frac{1}{5}\le x< \frac{-3}{4}+\frac{2}{7}-\frac{1}{4}+\frac{3}{5}+\frac{5}{7}\)
\(=\frac{1.10}{3.10}+\frac{-2.6}{5.6}+\frac{1.5}{6.5}-\frac{1.6}{5.6}\le x< \frac{-3.35}{4.35}+\frac{2.20}{7.20}-\frac{1.35}{4.35}+\frac{3.28}{5.28}+\frac{5.20}{7.20}\)
\(=\)\(\frac{10}{30}+\frac{-12}{30}+\frac{5}{30}-\frac{6}{30}\le x< \frac{-105}{140}+\frac{40}{140}-\frac{35}{140}+\frac{84}{140}+\frac{100}{140}\)
\(=\)\(\frac{10+\left(-12\right)+5-6}{30}\le x< \frac{-105+40-35+84+100}{140}\)
\(=\)\(\frac{-3}{30}\le x< \frac{84}{140}\)
\(=\)\(\frac{-3.14}{30.14}\le x< \frac{84.3}{140.3}\)
\(=\)\(\frac{-42}{420}\le x< \frac{252}{420}\)
\(\Rightarrow-42\le x< 252\)
\(\Rightarrow x=\left\{-42;-41;-41;...;249;250;251;252\right\}\)
Chúc bạn một buổi chiều vui vẻ ~! ❤‿❤
Nếu có sai gì thì báo lỗi với mình nhé!
Cái bước thứ hai từ dưới lên sai rồi nhé em! KHông đc vứt mẫu số như vậy :)
a) \(2x-\frac{2}{3}-7x=\frac{3}{2}-1\\ 2x-7x-\frac{2}{3}=\frac{1}{2}\\ -5x=\frac{1}{2}+\frac{2}{3}\\ -5x=\frac{7}{6}\\ x=\frac{7}{6}:\left(-5\right)\\ x=\frac{-7}{30}\)Vậy \(x=\frac{-7}{30}\)
b) \(\frac{3}{2}x-\frac{2}{5}=\frac{1}{3}x-\frac{1}{4}\\ \frac{3}{2}x-\frac{1}{3}x=\frac{2}{5}-\frac{1}{4}\\ \frac{7}{6}x=\frac{3}{20}\\ x=\frac{3}{20}:\frac{7}{6}\\ x=\frac{9}{70}\)Vậy \(x=\frac{9}{70}\)
c) \(\frac{2}{3}-\frac{5}{3}x=\frac{7}{10}x+\frac{5}{6}\\ \frac{2}{3}-\frac{5}{6}=\frac{7}{10}x+\frac{5}{3}x\\ \frac{-1}{6}=\frac{71}{30}x\\ x=\frac{-1}{6}:\frac{71}{30}\\ x=\frac{-5}{71}\)Vậy \(x=\frac{-5}{71}\)
d) \(2x-\frac{1}{4}=\frac{5}{6}-\frac{1}{2}x\\ 2x+\frac{1}{2}x=\frac{5}{6}+\frac{1}{4}\\ \frac{5}{2}x=\frac{13}{12}\\ x=\frac{13}{12}:\frac{5}{2}\\ x=\frac{13}{30}\)Vậy \(x=\frac{13}{30}\)
e) \(3x-\frac{5}{3}=x-\frac{1}{4}\\ 3x-x=\frac{5}{3}-\frac{1}{4}\\ 2x=\frac{17}{12}\\ x=\frac{17}{12}:2\\ x=\frac{17}{24}\)Vậy \(x=\frac{17}{24}\)
Èo, chăm thế? Chăm hơn cả mik cơ, gần 11 h rồi onl thì thấy bài được bạn HISI làm hết rồi :((
a) \(\frac{9}{20}\) c) \(\frac{-55}{4}\)
b) \(\frac{116}{75}\) d) \(\frac{-76}{45}\)
đúng hết đấy nhé mình tính kĩ lắm ko sai đâu
chúc may mắn