x+2/5+x+2/6+x+2/7=x+2/8+x+2/9
x+107/105=17/36
x=17/36-107/105
x=-689/1260
\(a.x+\frac{2}{5}+x+\frac{2}{6}+x+\frac{2}{7}=x+\frac{2}{8}+x+\frac{2}{9}\)
\(3x+\left(\frac{2}{5}+\frac{2}{6}+\frac{2}{7}\right)=2x+\left(\frac{2}{8}+\frac{2}{9}\right)\)
\(3x-2x=\left(\frac{2}{5}+\frac{2}{6}+\frac{2}{7}\right)-\left(\frac{2}{8}+\frac{2}{9}\right)\)
\(1x=\frac{689}{1260}=0,54\)
a, \(\frac{x+2}{5}+\frac{x+2}{6}+\frac{x+2}{7}=\frac{x+2}{8}+\frac{x+2}{9}\)
\(\Rightarrow\frac{x+2}{5}+\frac{x+2}{6}+\frac{x+2}{7}-\frac{x+2}{8}-\frac{x+2}{9}=0\)
\(\Rightarrow\left(x+2\right)\left(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)=0\)
Mà \(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\ne0\)
=> x + 2 = 0 => x = -2
Vậy x = -2
b, \(\frac{x+9}{1000}+\frac{x+8}{1001}=\frac{x+7}{1002}+\frac{x+6}{1003}\)
\(\Rightarrow\left(\frac{x+9}{1000}+1\right)+\left(\frac{x+8}{1001}+1\right)=\left(\frac{x+7}{1002}+1\right)+\left(\frac{x+6}{1003}+1\right)\)
\(\Rightarrow\frac{x+9+1000}{1000}+\frac{x+8+1001}{1001}=\frac{x+7+1002}{1002}+\frac{x+6+1003}{1003}\)
\(\Rightarrow\frac{x+1009}{1000}+\frac{x+1009}{1001}=\frac{x+1009}{1002}+\frac{x+1009}{1003}\)
\(\Rightarrow\frac{x+1009}{1000}+\frac{x+1009}{1001}-\frac{x+1009}{1002}-\frac{x+1009}{1003}=0\)
\(\Rightarrow\left(x+1009\right)\left(\frac{1}{1000}+\frac{1}{1001}-\frac{1}{1002}-\frac{1}{1003}\right)=0\)
Mà \(\frac{1}{1000}+\frac{1}{1001}-\frac{1}{1002}-\frac{1}{1003}\ne0\)
=> x + 1009 = 0 => x = -1009
Vậy x = -1009
