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\(A=\frac{2004x37+2004+2x2004+2004x59+2004}{324x321-201x324-324x101-18x324}\)
\(A=\frac{2004x\left(37+1+2+59+1\right)}{324x\left(321-201-101-18\right)}\)
\(A=\frac{2004x\left[\left(37+1+2\right)+\left(59+1\right)\right]}{324x\left[321-\left(201+101+18\right)\right]}\)
\(A=\frac{2004x\left(40+60\right)}{324x\left[321-320\right]}\)
\(A=\frac{2004x100}{324x1}=\frac{2004100}{324}=\frac{16700}{27}\)
Ta có : \(\frac{2004\times37+2004+2\times2004+2004\times49+2004}{324\times321-201\times324-324\times101-18\times324}\)
\(=\frac{2004\times\left(37+1+2+1+49\right)}{324\times\left(321-201-101-18\right)}\)
\(=\frac{2004\times90}{324\times1}=\frac{2004\times90}{324}=\frac{1670}{3}\)
\(B=\frac{2003+2004}{2004+2005}=\frac{2003}{2004+2005}+\frac{2004}{2004+2005}\)
Ta có: \(\frac{2003}{2004}>\frac{2003}{2004+2005}\)
\(\frac{2004}{2005}>\frac{2004}{2004+2005}\)
\(\frac{2003}{2004}+\frac{2004}{2005}>\frac{2003+2004}{2004+2005}\)
\(A>B\)
Vậy A>B
Ta có:
n = \(\frac{2003+2004}{2004+2005}\)
\(=>\) n = \(\frac{2003}{2004+2005}+\frac{2004}{2004+2005}\)
Vì \(\frac{2003}{2004}>\frac{2003}{2004+2005}\)
\(\frac{2004}{2005}>\frac{2004}{2004+2005}\)
\(=>\frac{2003}{2004}+\frac{2004}{2005}>\frac{2003}{2004+2005}+\frac{2004}{2004+2005}\)
\(=>\)m > n
Chúc bạn học tốt :)
A=\(\frac{16700}{27}\)