documentclass{article}
usepackage{geometry}%
usepackage{mathtools}
usepackage{eqparbox}
newcommand{eqmathbox}[2][M]{eqmakebox[#1]{$displaystyle#2$}}

begin{document}

begin{spreadlines}{1.5ex}
begin{alignat}{3}
 & & (L-epsilon)(x-M) & leq eqmathbox{f(x)-f(M)} & &leq(L+epsilon)(x-M)\
 & Rightarrowqquad & (L-epsilon)(x-M)+f(M)&leq eqmathbox{f(x)}& & leq(L+epsilon)(x-M)+f(M)\
 & Rightarrow & (L-epsilon)biggl(1-frac{M}{x}biggr)+frac{f(M)}{x}&leqeqmathbox{frac{f(x)}{x}} & &leqfrac{f(M)}{x}+(L+epsilon)biggl(1-frac{M}{x}biggr)
end{alignat}
end{spreadlines}