\(\frac{x+4}{2006}+\frac{x+3}{2007}=\frac{x+2}{2008}+\frac{x+1}{2009}\)
Tìm x
\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)
\(\frac{3}{\left(x+2\right).\left(x+5\right)}\)+\(\frac{5}{\left(x+5\right).\left(x+10\right)}\)+\(\frac{7}{\left(x+10\right).\left(x+5\right)}\)=\(\frac{x}{\left(x+2\right).\left(x+17\right)}\)
\(\frac{x-1}{2009}\)+ \(\frac{x-2}{2008}\)=\(\frac{x-3}{2007}\) + \(\frac{x-4}{2006}\)
a, Tính nhanh :
\(\frac{2009\times(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2007}+\frac{1}{2008})}{2008-\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{2006}{2007}+\frac{2007}{2008}\right)}\)
b, Cho \(\text{Q}=2+2^2+2^3+...+2^{10}\). Chứng tỏ rằng \(Q⋮3\).
\(S=\frac{2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}\)
S=?
a)\(\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}=\frac{x+1}{5}+\)\(\frac{x+1}{6}\)
b)\(\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\)\(\frac{x+10}{2000}+\frac{x+11}{1999}+\frac{x+12}{1998}\)
c)\(2.2^2.2^3.2^4.........2^x=1024\)\(\left(x\in z\right)\)
Tìm x
Giá trị của biểu thức \(A=\frac{2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}\)là \(A=.............\)
tìm x
a) \(\frac{x-1}{2}+\frac{x-2}{5}=\frac{1}{4}+\frac{x-7}{10}\)
b) \(3-\frac{2}{2x-3}=\frac{2}{5}+\frac{1}{2x-3}-\frac{3}{2}\)
c)\(7\cdot\left(x-1\right)+2x\cdot\left(1-x\right)=0\)
d) \(\frac{x+1}{2008}+\frac{x+2}{2017}+\frac{x+3}{2016}=\frac{x+10}{2009}+\frac{x+11}{2008}+\frac{x+12}{2007}\)
e) \(\frac{2}{\left(x-1\right)\cdot\left(x-3\right)}+\frac{5}{\left(x-3\right)\cdot\left(x-8\right)}+\frac{12}{\left(x-8\right)\cdot\left(x-20\right)}-\frac{1}{x-20}=\frac{-3}{4}\)