\(\eqalign{& B = {{ - 2} \over {17}} + {{15} \over {23}} + {{ - 15} \over {17}} + {4 \over {19}} + {8 \over {23}} \cr & = \left( {{{ - 2} \over {17}} + {{ - 15} \over {17}}} \right) + \left( {{{15} \over {23}} + {8 \over {23}}} \right) + {4 \over {19}} \cr & = \left( {{{ - 2 + ( - 15)} \over {17}}} \right) + \left( {{{15 + 8} \over {23}}} \right) + {4 \over {19}} \cr & = \left( {{{ - 17} \over 17}} \right) + \left( {{{23} \over {23}}} \right) + {4 \over 19} \cr & = \left( { - 1} \right) + 1 + {4 \over 19} = 0 + {4 \over {19}} = {4 \over {19}} \cr & C = {{ - 1} \over 2} + {3 \over {21}} + {{ - 2} \over 6} + {{ - 5} \over {30}} \cr & = {{ - 1} \over 2} + {1 \over 7} + {{ - 2} \over 6} + {{ - 1} \over 6} \cr & = {{ - 1} \over 2} + {1 \over 7} + \left( {{{ - 2} \over 6} + {{ - 1} \over 6}} \right) \cr & = {{ - 1} \over 2} + {1 \over 7} + {{ - 3} \over 6} \cr & = {{ - 1} \over 2} + {1 \over 7} + {{ - 1} \over 2} \cr & = \left( {{{ - 1} \over 2} + {{ - 1} \over 2}} \right) + {1 \over 7} \cr & = {{ - 2} \over 2} + {1 \over 7} \cr & = - 1 + {1 \over 7} = {{ - 7} \over 7} + {1 \over 7} \cr & = {{ - 7 + 1} \over 7} = {{ - 6} \over 7} \cr} \)
