Thực hiện các phép tính sau:
a) \({{{c^2} - {d^2}} \over {{c^2} - 2cd + {d^2}}}:{1 \over {cd + {d^2}}}\) ;
b) \({{{m^2} - 4} \over {{m^2} - 3m + 2}}:{m \over {m - 1}}\) ;
c) \({{{m^2} - 9} \over {{m^2} + m + 1}}:(m - 3)\) ;
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d) \((m - 1):{{{m^2}} \over {{{(m - 1)}^2}}}\) .
\(\eqalign{ & a)\,\,{{{c^2} - {d^2}} \over {{c^2} - 2cd + {d^2}}}:{1 \over {cd + {d^2}}} = {{\left( {c - d} \right)\left( {c + d} \right)} \over {{{\left( {c - d} \right)}^2}}}.\left( {cd + {d^2}} \right) \cr & = {{\left( {c + d} \right)d\left( {c + d} \right)} \over {c - d}} = {{{{\left( {c + d} \right)}^2}d} \over {c - d}} \cr & b)\,\,{{{m^2} - 4} \over {{m^2} - 3m + 2}}:{m \over {m - 1}} = {{{m^2} - 4} \over {{m^2} - 3m + 2}}.{{m - 1} \over m} \cr & = {{\left( {m - 2} \right)\left( {m + 2} \right)\left( {m - 1} \right)} \over {\left( {{m^2} - 3m + 2} \right).m}} = {{\left( {m - 2} \right)\left( {m + 2} \right)\left( {m - 1} \right)} \over {\left( {m - 1} \right)\left( {m - 2} \right)m}} = {{m + 2} \over m} \cr & c)\,\,{{{m^2} - 9} \over {{m^2} + m + 1}}:\left( {m - 3} \right) = {{{m^2} - 9} \over {{m^2} + m + 1}}.{1 \over {m - 3}} \cr & = {{\left( {m - 3} \right)\left( {m + 3} \right)} \over {\left( {{m^2} + m + 1} \right)\left( {m - 3} \right)}} = {{m + 3} \over {{m^2} + m + 1}} \cr & d)\,\,\left( {m - 1} \right):{{{m^2}} \over {{{\left( {m - 1} \right)}^2}}} = \left( {m - 1} \right).{{{{\left( {m - 1} \right)}^2}} \over {{m^2}}} = {{{{\left( {m - 1} \right)}^3}} \over {{m^2}}} \cr} \)