Tính nhanh:
\({\rm{A}} = {5 \over {13}} + {{ – 5} \over 7} + {{ – 20} \over {41}} + {8 \over {13}} + {{ – 21} \over {41}}\)
\(B = {{ – 5} \over 9} + {8 \over {15}} + {{ – 2} \over {11}} + {4 \over { – 9}} + {7 \over {15}}\)
Giải
\(\eqalign{
& {\rm{A}} = {5 \over {13}} + {{ – 5} \over 7} + {{ – 20} \over {41}} + {8 \over {13}} + {{ – 21} \over {41}} \cr
& = \left( {{5 \over {13}} + {8 \over {13}}} \right) + \left( {{{ – 20} \over {41}} + {{ – 21} \over {41}}} \right) + {{ – 5} \over 7} \cr
& = 1 + \left( { – 1} \right) + {{ – 5} \over 7} = {{ – 5} \over 7} \cr} \)
\(\eqalign{
& B = {{ – 5} \over 9} + {8 \over {15}} + {{ – 2} \over {11}} + {4 \over { – 9}} + {7 \over {15}} \cr
& = \left( {{{ – 5} \over 9} + {{ – 4} \over 9}} \right) + \left( {{8 \over {15}} + {7 \over {15}}} \right) + {{ – 2} \over {11}} \cr
& = – 1 + 1 + {{ – 2} \over {11}} = {{ – 2} \over {11}} \cr} \)