\(4+\frac{1}{x}=\frac{4x+1}{x}\)

\(\frac{1}{4+\frac{1}{x}}=\frac{x}{4x+1}\)

\(3+\frac{1}{4+\frac{1}{x}}=3+\frac{x}{4x+1}=\frac{13x+3}{4x+1}\)

Tương tự Vế Trái sẽ tìm đc

\(21+\frac{12\left(13x+3\right)}{30x+7}\)

Vế phải bấm máy tính nhá casio mà

\(VP=\frac{104052}{137}=21+\frac{101175}{137}\)

Suy ra 

\(\frac{156x+36}{30x+7}=\frac{101175}{137}\Leftrightarrow21375x+4932=3035250x+708225\)

\(\Leftrightarrow1004625x=-234431\Leftrightarrow x=-\frac{234431}{1004625}\)

a) \(\frac{x}{3}-\frac{10}{21}=-\frac{1}{7}\)

\(\Rightarrow\frac{x}{3}=-\frac{1}{7}+\frac{10}{21}\)

\(\Rightarrow\frac{x}{3}=\frac{7}{21}\)

\(\Rightarrow\frac{x}{3}=\frac{1}{3}\)

\(\Rightarrow x=1\)

\(x-25\%=\frac{1}{2}\)

\(\Rightarrow x-\frac{1}{4}=\frac{1}{2}\)

\(\Rightarrow x=\frac{1}{2}+\frac{1}{4}\)

\(\Rightarrow x=\frac{3}{4}\)

c) \(-\frac{5}{6}+\frac{8}{3}+-\frac{29}{6}\le x\le-\frac{1}{2}+2+\frac{5}{2}\)

\(\Rightarrow-3\le x\le4\)

\(\Rightarrow x\in\left\{-3;-2;-1;0;1;2;3;4\right\}\)

a)x/3-10/21=-1/7

 x/3=-1/7+10/21

x/3=1/3

=> x= 1

b/ x-25%=1/2

      x-1/4=1/2

             x=1/2+1/4

             x=3/4

a)\(\left(2x-3\right)\left(x+1\right)< 0\)

\(\Leftrightarrow\begin{cases}2x-3>0\\x+1< 0\end{cases}\)  hoặc \(\begin{cases}2x-3< 0\\x+1>0\end{cases}\)

\(\Leftrightarrow\begin{cases}x>\frac{3}{2}\\x< -1\end{cases}\) (loại)  hoặc \(\begin{cases}x< \frac{3}{2}\\x>-1\end{cases}\)

\(\Leftrightarrow-1< x< \frac{3}{2}\)

b) \(\left(x-\frac{1}{2}\right)\left(x+3\right)>0\)

\(\Leftrightarrow\begin{cases}x-\frac{1}{2}>0\\x+3>0\end{cases}\) hoặc \(\begin{cases}x-\frac{1}{2}< 0\\x+3< 0\end{cases}\)

\(\Leftrightarrow\begin{cases}x>\frac{1}{2}\\x>-3\end{cases}\) hoặc \(\begin{cases}x< \frac{1}{2}\\x< -3\end{cases}\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x>\frac{1}{2}\\x< -3\end{array}\right.\)

c) Sai đề phải là \(\frac{x}{\left(x+3\right)\left(x+7\right)}\)

Có: \(\frac{3}{\left(x+3\right)\left(x+5\right)}+\frac{5}{\left(x+5\right)\left(x+10\right)}+\frac{7}{\left(x+10\right)\left(x+17\right)}=\frac{x}{\left(x+3\right)\left(x+17\right)}\)

\(\Leftrightarrow\)\(\frac{1}{x+3}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+10}+\frac{1}{x+10}-\frac{1}{x+7}=\frac{x}{\left(x+3\right)\left(x+7\right)}\)

\(\Leftrightarrow\)\(\frac{1}{x+3}-\frac{1}{x+7}=\frac{x}{\left(x+3\right)\left(x+7\right)}\)

\(\Leftrightarrow\)\(\frac{4}{\left(x+3\right)\left(x+7\right)}=\frac{x}{\left(x+3\right)\left(x+7\right)}\)

\(\Leftrightarrow x=4\)

đề câu c sai rầu kìa má

=>\(\frac{6\left(x-1\right)}{18}+\frac{9\left(3x-5\right)}{18}+\frac{2\left(2x\right)}{18}+\frac{2\left(-5x+3\right)}{18}=\frac{1}{2}\)

=>\(\frac{6x-6}{18}+\frac{27x-45}{18}+\frac{4x}{18}+\frac{-10x+6}{18}=\frac{1}{2}\)

=>\(\frac{\left(6x-6\right)+\left(27x-45\right)+4x+\left(-10x+6\right)}{18}=\frac{1}{2}\)

=>\(\frac{27x-45}{18}=\frac{1}{2}\)

=>54x-90=18

54x =108

=>x=2

quy đồng lên rồi nhân chéo rồi giải

x=2

x=2 nhớ k  cho mình nha

a.\(\Rightarrow\left(\frac{3}{5}+x\right):\frac{2}{7}=\frac{3}{35}-\frac{2}{7}\)

\(\Rightarrow\left(\frac{3}{5}+x\right):\frac{2}{7}=-\frac{1}{5}\)

\(\Rightarrow\frac{3}{5}+x=-\frac{1}{5}.\frac{2}{7}\)

\(\Rightarrow\frac{3}{5}+x=-\frac{2}{35}\)

\(\Rightarrow x=-\frac{2}{35}-\frac{3}{5}\)

Vậy \(x=-\frac{23}{35}\).

b. => 5x-1=0                hoặc 2x-1/3=0

=> 5x=1                       hoặc 2x=1/3

=> x=1/5                      hoặc x=1/6

c. \(\Rightarrow\frac{1}{7}:x=\frac{3}{14}-\frac{3}{7}\)

\(\Rightarrow\frac{1}{7}:x=-\frac{3}{14}\)

\(\Rightarrow x=\frac{1}{7}:\left(-\frac{3}{14}\right)\)

Vậy \(x=\frac{-2}{3}\).