[latex]frac{ab}{ab+b^{2} } = frac{2009}{2010}[/latex] a) [latex]frac{a}{b}[/latex] [latex]frac{ab}{ab+b^{2} } = frac{2009}{2010}[/latex] [latex]frac{ab}{b(a+b)} = frac{2009}{2010}[/latex] [latex]frac{a}{a+b} = frac{2009}{2010}[/latex] [latex]frac{a+b}{a}= frac{2010}{2009}[/latex] [latex]frac{a}{a}+ frac{b}{a}= frac{2010}{2009}[/latex] [latex]1+ frac{b}{a}= frac{2010}{2009}[/latex] [latex]frac{b}{a}= frac{2010}{2009}-1[/latex] [latex]frac{b}{a}= frac{2010}{2009}-frac{2009}{2009}[/latex] [latex]frac{b}{a}= frac{1}{2009}[/latex] [latex]frac{a}{b}= 2009[/latex] ================== b) [latex]frac{b}{a+b}= frac{1}{ frac{a+b}{b}}= frac{1}{ frac{a}{b}+ frac{b}{b} }= frac{1}{ frac{a}{b}+ 1}= frac{1}{2009+ 1}= frac{1}{2010}[/latex] ================== c) [latex]frac{ a^{2} +ab}{ab}=frac{ a(a+b) }{ab}=frac{ a+b}{b}= frac{1}{frac{b}{a+b}}= frac{1}{frac{1}{2010}} =2010[/latex]
