Given that f(x) = x^{-1} + x/(1 + x^{-1}), f(f(-2))? Express your answer as a common fraction.
+129840 f (x) = 1/x + x/[ 1 + 1/x ] = 1/x + x / ( [x + 1] /x ) = 1/x + x^2 / (x + 1)
f(-2) = -1/2 + (-2)^2 / (-1) = -4 -1/2 = -9/2
f (f (-2)) = f (-9/2) = 1/ (-9/2) + (-9/2)^2 / ( -9/2 + 1) =
-2/9 + ( 81/4) /( -7/2) =
-2/9 - (81/4) (2/7) =
-2/9 - 162 / 28 =
-2/9 - 81/14 =
-757 / 126
