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\(A=1-\frac{1}{2014x2015}\)
\(B=1-\frac{1}{2015x2016}\)
\(2014x2015< 2015x2016\Rightarrow\frac{1}{2014x2015}>\frac{1}{2015x2016}\Rightarrow A< B\)
\(\frac{2012+2013x2014}{2014x2015-2016}\)
= \(\frac{2012+4054182}{4058210-2016}\)
= \(\frac{4056194}{4056194}\)
= \(\frac{1}{1}\)
= \(1\)
Answer : \(1\)
\(\frac{2012+2013.2014}{2014.2015-2016}\)
\(=\frac{2012+2013.2014}{2014.\left(2013+2\right)-2016}\)
\(=\frac{2012+2013.2014}{2014.2013+2014.2-2016}\)
\(=\frac{2012}{4028-2016}\)
\(=\frac{2012}{2012}\)
\(=1\)
\(\frac{2012+2013x2014}{2014x2015-2016}\)\(=\frac{2012+2013x2014}{2014x\left(2013+2\right)-2016}\)
\(=\frac{2012+2013x2014}{2014x2013+4028-2016}\)
\(=\frac{2012+2013x2014}{2014x2013+2012}\)
\(=1\)
\(\frac{2012+2013x2014}{2014x2015-2016}\)
= \(\frac{2012+2013x2014}{2014x\left(2013+2\right)-2016}\)
= \(\frac{2012+2013x2014}{2014x2013+4028-2016}\)
= \(\frac{2012+2013x2014}{2014x2013+2012}\)
= 1
=13+2013x2014/2014x2013+2013-2000
=13+2014x2013/2014x2013+13
=1
=[2013*2014*+2014*2015+2015*2016]*[\(1\frac{1}{3}-1\frac{1}{3}\)]
=A*0
=0
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