(X + 3 phần 5 ) nhân ( X + 1 ) < 0
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x-1}{3}\cdot\frac{x+2}{5}>0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)>0\)
\(TH1:\orbr{\begin{cases}x-1>0\\x+2>0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x>1\\x>-2\end{cases}}\Leftrightarrow x>1\left(1\right)\)
\(TH2:\orbr{\begin{cases}x-1< 0\\x+2< 0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x< 1\\x< -2\end{cases}}\Leftrightarrow x< -2\left(2\right)\)
Tu ( 1 ) va ( 2 ) suy ra \(-2< x< 1\)
Cho mik sua 1 chut nha.
\(TH1:\Leftrightarrow x>-2\)
\(TH2:\Leftrightarrow x< 1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x-\frac{1}{3}\right)\left(x+\frac{2}{5}\right)>0\)
\(\orbr{\begin{cases}x=\frac{1}{3}\\x=-\frac{2}{5}\end{cases}}\)
\(-\frac{2}{5}< x< \frac{1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{3}{4}x-\frac{9}{16}\right)-\left(\frac{1}{3}+\frac{-3}{5}x\right)=0.\)
\(\frac{3}{4}x-\frac{9}{16}-\frac{1}{3}-\frac{-3}{5}x=0\)
\(\frac{27}{20}x-\frac{43}{48}=0\)
\(\frac{27}{20}x=\frac{43}{48}\)
\(x=\frac{215}{324}\)
mong ủng hộ mk
(3 phần 4 nhân X - 9 phần 16 ) - (1 phần 3 + -3 phần 5 chia X ) = 0
=>\(\frac{3}{4}.x-\frac{9}{16}=\frac{1}{3}+\frac{-3}{5}:x\)
=\(\frac{3}{4}.x-\frac{9}{16}=\frac{-4}{15}:x\)
=>\(\frac{3}{4}.x-\frac{-4}{15}:x=\frac{9}{16}\)
Đến đây thì mk chịu =)
Dù sao thi cg ti.ck giúp mk tí
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{11}{75}\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{11}{75}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{x+2}=\frac{11}{75}:\frac{1}{2}=\frac{22}{75}\Leftrightarrow\frac{1}{x+2}=\frac{1}{25}\Leftrightarrow x=23\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ý bạn bảo (x-2 và 1 phần 2) là hợp số hả :
ta có (x-2 và 1 phần 2) nhân (2x+3 và 1 phần 5) =0
\(\Leftrightarrow\) [2.(x-2) +1]. [5.(2x+3)+1]=0
\(\Leftrightarrow\)(2x-3)(10x+16)=0
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x=3\\10x=-16\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{-8}{5}\end{cases}}\)
vậy
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{3}-\frac{1}{3}.\frac{x-3}{2}-\frac{1}{2}.2.x+1=5\)
\(\Leftrightarrow\frac{2}{3}-\frac{x-3}{3.2}-\frac{2.x}{2}+1=5\)
\(\Leftrightarrow\frac{2}{3}-\frac{x-3}{6}-x+1=5\)
\(\Leftrightarrow\frac{2}{3}-\frac{x-3}{6}-x=4\)
\(\Leftrightarrow\frac{4}{6}-\frac{x-3}{6}-\frac{6x}{6}=4\)
\(\Leftrightarrow\frac{4-\left(x-3\right)-6x}{6}=4\)
\(\Leftrightarrow\frac{4-x+3+6x}{6}=4\)
\(\Leftrightarrow\frac{4+3-x+6x}{6}=\frac{4}{1}\)
\(\Leftrightarrow\frac{7+5x}{6}=\frac{4}{1}\)
\(\Leftrightarrow7+5x=4.6\)
\(\Leftrightarrow7+5x=24\)
\(\Leftrightarrow5x=24-7\)
\(\Leftrightarrow5x=17\)
\(\Leftrightarrow x=\frac{17}{5}\)
Vậy \(x=\frac{17}{5}\)
Chúc bạn học tốt
\(\frac{x+3}{5}\cdot\left(x+1\right)< 0\)
\(\Leftrightarrow\left(x+3\right)\left(x+1\right)< 0\)
\(TH1:\orbr{\begin{cases}x+3< 0\\x+1>0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x< -3\\x>-1\end{cases}}\Leftrightarrow-1< x< 3\)
\(TH2:\orbr{\begin{cases}x+3>0\\x+1< 0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x>-3\\x< -1\end{cases}}\Leftrightarrow-3< x< 1\)
\(\frac{x+3}{5}\cdot\left(x+1\right)< 0\)
\(\Leftrightarrow\frac{\left(x+3\right)\left(x+1\right)}{5}< 0\)
\(\Leftrightarrow\left(x+3\right)\left(x+1\right)< 0\)
Nên x+3 và x+1 phải trái dấu,mà x+1<x+3
Do đó x+1 sẽ <0
\(\Leftrightarrow\hept{\begin{cases}x+1< 0\\x+3>0\end{cases}\Leftrightarrow\hept{\begin{cases}x< -1\\x>-3\end{cases}\Leftrightarrow}}-3< x< -1\)