\(a,\Leftrightarrow5\left(x-2\right)-15x\le9+10\left(x+1\right)\)

\(\Leftrightarrow5x-10-15x\le9+10x+10\)

\(\Leftrightarrow-20x\le29\)

\(\Leftrightarrow x\ge-1,45\)

Vậy ...........

\(b,\Rightarrow\left(x+2\right)-3\left(x-3\right)=5\left(x-2\right)\)

\(\Leftrightarrow x+2-3x+9-5x+10=0\)

\(\Leftrightarrow-7x+21=0\)

\(\Leftrightarrow x=3\)

Vậy ..............

 \(\frac{x-2}{6}-\frac{x}{2}\le\frac{3}{10}+\frac{x+1}{3}\Leftrightarrow\frac{5\left(x-2\right)}{30}-\frac{15x}{30}\le\frac{9}{30}+\frac{10\left(x+1\right)}{30}\)

\(\Leftrightarrow5x-10-15x-9-10x-10\le0\) 

 \(\Leftrightarrow-20x-29\le0\Leftrightarrow\left(-20x\right)\cdot\frac{-1}{20}\ge29\cdot-\frac{1}{20}\)

 \(\Leftrightarrow x\ge-\frac{29}{20}\)

ĐKXĐ : \(\hept{\begin{cases}x\ne2\\x\ne3\end{cases}}\)

\(\frac{x+2}{x^2-5x+6}-\frac{3}{x-2}=\frac{5}{x-3}\) 

 \(\Rightarrow\frac{x+2}{x-2x-3x+6}-\frac{3}{x-2}=\frac{5}{x-3}\)

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

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

 \(\Rightarrow x+2-3x+9-5x+10=0\)

\(\Leftrightarrow-7x+21=0\Leftrightarrow x=3\) (nhân)

 tập nghiệm của phương trình là S= 3

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

\(\Leftrightarrow2x-\frac{x}{2}+\frac{3+x}{4}=6-\frac{1}{2}+\frac{6-x}{6}\)

\(\Leftrightarrow24x-6x+9+3x=72-6+12-2x\)

\(\Leftrightarrow23x=69\)

\(\Leftrightarrow x=3\)

Vậy nghiệm của pt x=3

ĐK: x \(\ne\)-1; x \(\ne\)2

\(\frac{x+2}{x+1}+\frac{3}{x-2}=\frac{3}{x^2-x-2}+1\)

<=> \(\frac{\left(x+2\right)\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}+\frac{3\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\frac{3}{\left(x+1\right)\left(x-2\right)}+\frac{\left(x+1\right)\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}\)

<=>  x² - 4 + 3x + 3 = 3 + x² - x - 2

<=> x² + 3x - x² + x = 1 + 1

<=> 4x = 2

<=> x = 1/2

Vậy S = {1/2}

x=-0,44

\(x+\frac{x+1}{2}+\frac{x+2}{3}+\frac{x+3}{4}=1\)

\(\Rightarrow\frac{12x}{12}+\frac{6x+6}{12}+\frac{4x+8}{12}+\frac{3x+9}{12}=\frac{12}{12}\)

\(\Rightarrow25x+23=12\)

\(\Rightarrow x=\frac{-11}{25}\)

\(x+\frac{x+1}{2}+\frac{x+2}{3}+\frac{x+3}{4}=1\)

\(\Rightarrow\frac{12x+6\left(x+1\right)+4\left(x+2\right)+3\left(x+3\right)}{12}=1\)

\(\Rightarrow\frac{12x+6x+6+4x+8+3x+9}{12}=1\)

\(\Rightarrow\frac{25x+23}{12}=1\Rightarrow25x+23=12\Rightarrow x=-\frac{11}{25}\)

Vậy \(x=-\frac{11}{25}\)

- Các bạn bỏ giùm mình số 2 cuối nhé. Chỉ có 1 số 2 thôi.

\(\frac{x+2}{x+1}-\frac{3}{2-x}=\frac{-3}{\left(x+1\right)\left(x-2\right)}+2\)(1)

ĐKXĐ : \(x\ne-1;x\ne\pm2\)

Quy đồng và khử mẫu phương trình (1) , ta được :

\(\left(x+2\right)\left(2-x\right)\left(x-2\right)-3\left(x+1\right)\left(x-2\right)=-3\left(2-x\right)+2\left(x+1\right)\left(x-2\right)\left(2-x\right)\)

\(\Leftrightarrow-\left(x+2\right)\left(x-2\right)^2-3\left(x^2-x-2\right)=-6+3x-2\left(x+1\right)\left(x^2-4x+4\right)\)

\(\Leftrightarrow-\left(x-2\right)\left(x^2-4\right)-3x^2+3x+6=-6+3x-2\left(x^3-3x^2+4\right)\)

\(\Leftrightarrow-x^3+2x^2+4x-8-3x^2+3x+6=-6+3x-2x^3+6x^2-8\)

\(\Leftrightarrow-x^3-x^2+7x-2+6-3x+2x^3-6x^2+8=0\)

\(\Leftrightarrow x^3-7x^2+4x+12=0\)

\(\Leftrightarrow x^3-2x^2-5x^2+10x-6x+12=0\)

\(\Leftrightarrow x^2\left(x-2\right)-5x\left(x-2\right)-6\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^2+x-6x-6\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x\left(x+1\right)-6\left(x+1\right)\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x-6\right)\left(x+1\right)=0\)

\(\Leftrightarrow x=2\)(loại) ; \(x=6\)(chọn ) ; \(x=-1\)(loại).

Vậy S={6}.

a) \(\frac{x-1}{2}+\frac{x-2}{3}+\frac{x-3}{4}=\frac{x-4}{5}+\frac{x-5}{6}\)

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

\(\frac{x-1}{2}+\frac{x-1}{3}+\frac{x-1}{4}=\frac{x-1}{5}+\frac{x-1}{6}\)

\(\left(x-1\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)\)=0

\(x-1=0\)

\(x=1\)

phương trình tương đương với 1+\(\frac{1}{x}+1+\frac{1}{x+3}\)=1+\(\frac{1}{x+1}+1+\frac{1}{x+2}\)\(\Leftrightarrow\frac{1}{x}+\frac{1}{x+3}=\frac{1}{x+2}+\frac{1}{x+1}\)

\(\Leftrightarrow\frac{2x+3}{x\left(x+3\right)}=\frac{2x+3}{\left(x+1\right)\left(x+2\right)}\)\(\Leftrightarrow\left(2x+3\right)\left(\frac{1}{x\left(x+3\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\)=0

\(\Leftrightarrow\left(2x+3\right)\left(\frac{\left(x+1\right)\left(x+2\right)-x\left(x+3\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\right)=0\)

\(\Leftrightarrow\left(2x+3\right)\left(\frac{2}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\right)=0\)\(\Leftrightarrow2x+3=0\Leftrightarrow x=\frac{-3}{2}\)