\(x-\frac{6}{7}+x-\frac{7}{8}+x-\frac{8}{9}=x-\frac{9}{10}+x-\frac{10}{11}+x-\frac{11}{12}\)

\(x+x+x-x-x-x=\frac{6}{7}+\frac{7}{8}+\frac{8}{9}-\frac{9}{10}-\frac{10}{11}-\frac{11}{12}\)

\(0=\frac{6}{7}+\frac{7}{8}+\frac{8}{9}-\frac{9}{10}-\frac{10}{11}-\frac{11}{12}\)

X triệt tiêu hết ròi! Vậy đề bài yêu cầu tìm gì vậy. Nhưng mà...giá trị của 2 vế ko bằng nhau.

\(\Leftrightarrow\left(\frac{x+1}{7}-1\right)+\left(\frac{x+1}{8}-1\right)+\left(\frac{x+1}{9}-1\right)=\left(\frac{x+1}{10}-1\right)+\left(\frac{x+1}{11}-1\right)+\left(\frac{x+1}{12}-1\right)\)

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)=0\)

\(\text{Vì}\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\ne\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\)\(\Rightarrow\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\ne0\)

\(\Rightarrow x+1=0\)

\(\Rightarrow x=-1\)

\(\dfrac{8}{x}-8+\dfrac{11}{x}-11=\dfrac{9}{x}-9+\dfrac{10}{x}-10\)\(\Leftrightarrow\dfrac{8}{x}+\dfrac{11}{x}-\dfrac{9}{x}-\dfrac{10}{x}=8+11-9-10\)

\(\Leftrightarrow\dfrac{8+11-9-10}{x}=0\)

\(\Leftrightarrow\dfrac{0}{x}=0\)

\(\Leftrightarrow x=0\)

S=\(\left\{0\right\}\)

\(\Leftrightarrow\frac{x-6}{7}+1+\frac{x-7}{8}+1+\frac{x-8}{9}+1=\frac{x-9}{10}+1+\frac{x-10}{11}+1\)\(+\frac{x-11}{12}+1\) ( cộng 2 vế với 3 )

\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)

\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)=0\)

\(\Leftrightarrow x+1=0\) \(\left(do\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\ne0\right)\)

\(\Leftrightarrow x=-1\)

|x-10| = x+6

ĐKXĐ \(x\ne8;x\ne11;x\ne9;x\ne10\)

\(\dfrac{8}{x-8}+\dfrac{11}{x-11}=\dfrac{9}{x-9}+\dfrac{10}{x-10}\)

\(\Leftrightarrow\left(\dfrac{8}{x-8}+1\right)+\left(\dfrac{11}{x-11}+1\right)=\left(\dfrac{9}{x-9}+1\right)+\left(\dfrac{10}{x-10}+1\right)\)

\(\Leftrightarrow\dfrac{x}{x-8}+\dfrac{x}{x-11}=\dfrac{x}{x-9}+\dfrac{x}{x-10}\)

\(\Leftrightarrow\dfrac{x}{x-8}+\dfrac{x}{x-11}-\dfrac{x}{x-9}-\dfrac{x}{x-10}=0\)

\(\Leftrightarrow x\left(\dfrac{1}{x-8}+\dfrac{1}{x-11}-\dfrac{1}{x-9}-\dfrac{1}{x-10}\right)=0\)

\(\Leftrightarrow x=0\) hoặc \(\dfrac{1}{x-8}+\dfrac{1}{x-11}-\dfrac{1}{x-9}-\dfrac{1}{x-10}=0\)

1) x=0

2) \(\dfrac{1}{x-8}+\dfrac{1}{x-11}-\dfrac{1}{x-9}-\dfrac{1}{x-10}=0\)

\(\Leftrightarrow\dfrac{x-11+x-8}{\left(x-8\right)\left(x-11\right)}-\dfrac{x-10+x-9}{\left(x-9\right)\left(x-10\right)}=0\)

\(\Leftrightarrow\dfrac{2x-19}{\left(x-8\right)\left(x-11\right)}=\dfrac{2x-19}{\left(x-9\right)\left(x-10\right)}\)

\(\Leftrightarrow\dfrac{2x-19}{x^2-19x+88}=\dfrac{2x-19}{x^2-19x+90}\)

do \(x^2-19x+88\ne x^2-19x+90\)

\(\Rightarrow2x-19=0\)

=> x=\(\dfrac{19}{2}\)

Vậy x=\(0\); x=\(\dfrac{19}{2}\)

Tik

B

Chọn B

\(\frac{x}{10}=\frac{y}{6}=\frac{z}{21}\)và \(5x+y-2z=28\)

X=0

Xin slot :)

\(x\ne8;9;10;11\)

\(\frac{8}{x-8}+1+\frac{11}{x-11}+1=\frac{9}{x-9}+1+\frac{10}{x-10}+1\)

\(\Leftrightarrow\frac{x}{x-8}-\frac{x}{x-9}+\frac{x}{x-11}-\frac{x}{x-10}=0\)

\(\Leftrightarrow x\left(\frac{1}{x-8}-\frac{1}{x-9}+\frac{1}{x-11}-\frac{1}{x-10}\right)=0\)

\(\Leftrightarrow x\left(\frac{-1}{\left(x-8\right)\left(x-9\right)}+\frac{1}{\left(x-11\right)\left(x-10\right)}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\frac{-1}{\left(x-8\right)\left(x-9\right)}+\frac{1}{\left(x-11\right)\left(x-10\right)}=0\left(1\right)\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow\frac{1}{\left(x-8\right)\left(x-9\right)}=\frac{1}{\left(x-11\right)\left(x-10\right)}\Leftrightarrow\left(x-8\right)\left(x-9\right)=\left(x-11\right)\left(x-10\right)\)

\(\Leftrightarrow x^2-17x+72=x^2-21x+110\Leftrightarrow4x=38\Rightarrow x=\frac{19}{2}\)

\(\frac{1}{9x10}\)\(+\frac{1}{10x11}\)\(+\frac{1}{11x12}\)\(+.....\)\(+\frac{1}{805x806}\)

\(=\frac{1}{9}\)\(-\frac{1}{10}\)\(+\frac{1}{10}\)\(-\frac{1}{11}\)\(+\frac{1}{11}\)\(-\frac{1}{12}\)\(+.....\frac{1}{805}\)\(-\frac{1}{806}\)

\(=\frac{1}{9}\)\(-\frac{1}{806}\)

\(=\frac{797}{7254}\)

9 x 9 = 81

10 x 10 = 100

22 x 11 =242

9 x 9 = 81

10 x 10 = 100

22 x 11 = 242

~ Hok tốt ~

9 x 9 = 81

10 x 10 = 100

22 x 11 = 242