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p. 127:  3, 11

11.) $d'(x, y) + d'(y, z)  = {d(x, y) \over 1 + d(x, y)} + {d(y, z)
\over 1 + d(y, z)} = {d(x, y)[1 + d(y, z)] + d(y, z)[1 + d(x, y)]
\over [1 + d(x, y)][ 1 + d(y, z)]} = {d(x, y) + d(x, y)d(y, z) + d(y,
z) + d(y, z)d(x, y)] \over 1 + d(x, y) + d(y, z) + d(x, y)d(y, z)}$



12.) $d'(x, y) - d'(y, z) $

$= {d(x, y) \over 1 + d(x, y)} - {d(y, z) \over 1 + d(y, z)}$

$= {d(x, y)[1 + d(y, z)] - d(y, z)[1 + d(x, y)] \over [1 + d(x, y)][
1 + d(y, z)]}$

$= {d(x, y) + d(x, y)d(y, z) - d(y, z) - d(y, z)d(x, y) \over
1 + d(x, y) + d(y, z) + d(x, y)d(y, z)}$

$= {d(x, y) - d(y, z) \over
1 + d(x, y) + d(y, z) + d(x, y)d(y, z)}$

$\leq  {d(x, z) \over 1 +  d(x, y) + d(y, z)}  $

$\leq  {d(x, z) \over 1 + d(x, z)}$

$d(x, y) \leq d(x, z)  + d(y, z)$

$d(x, y) - d(y, z) \leq d(x, z)$

\end