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Tìm mẫu thức chung rồi thực hiện phép tính:
a) \({4 \over {2 + y}} + {2 \over {y – 2}} + {{5y – 6} \over {4 – {y^2}}}\) ;
b) \({{1 – 3m} \over {2m}} + {{3m – 2} \over {2m – 1}} + {{3m – 2} \over {2m – 4{m^2}}}\) ;
c) \({k \over {{k^2} – 9}} + {1 \over {6k – 9 – {k^2}}} + {1 \over {{k^2} + 6k + 9}}\) .
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\(\eqalign{ & a)\,\,{4 \over {2 + y}} + {2 \over {y – 2}} + {{5y – 6} \over {4 – {y^2}}} \cr & \,\,\,\,\, = {4 \over {2 + y}} + {{ – 2} \over {2 – y}} + {{5y – 6} \over {\left( {2 – y} \right)\left( {2 + y} \right)}} \cr & \,\,\,\,\, = {{4\left( {2 – y} \right)} \over {\left( {2 + y} \right)\left( {2 – y} \right)}} + {{ – 2\left( {2 + y} \right)} \over {\left( {2 – y} \right)\left( {2 + y} \right)}} + {{5y – 6} \over {\left( {2 – y} \right)\left( {2 + y} \right)}} \cr & \,\,\,\,\, = {{8 – 4y – 4 – 2y + 5y – 6} \over {\left( {2 – y} \right)\left( {2 + y} \right)}} \cr & \,\,\,\,\, = {{ – y – 2} \over {\left( {2 – y} \right)\left( {2 + y} \right)}} = {{ – \left( {y + 2} \right)} \over {\left( {2 – y} \right)\left( {2 + y} \right)}} = {{ – 1} \over {2 – y}} \cr & b)\,\,{{1 – 3m} \over {2m}} + {{3m – 2} \over {2m – 1}} + {{3m – 2} \over {2m – 4{m^2}}} \cr & \,\,\,\,\, = {{1 – 3m} \over {2m}} + {{ – \left( {3m – 2} \right)} \over {1 – 2m}} + {{3m – 2} \over {2m\left( {1 – 2m} \right)}} \cr & \,\,\,\,\, = {{\left( {1 – 3m} \right)\left( {1 – 2m} \right)} \over {2m\left( {1 – 2m} \right)}} + {{ – \left( {3m – 2} \right).2m} \over {2m\left( {1 – 2m} \right)}} + {{3m – 2} \over {2m\left( {1 – 2m} \right)}} \cr & \,\,\,\,\, = {{1 – 2m – 3m + 6{m^2} – 6{m^2} + 4m + 3m – 2} \over {2m\left( {1 – 2m} \right)}} \cr & \,\,\,\,\, = {{2m – 1} \over {2m\left( {1 – 2m} \right)}} = {{ – \left( {1 – 2m} \right)} \over {2m\left( {1 – 2m} \right)}} = {{ – 1} \over {2m}} \cr & c)\,\,{k \over {{k^2} – 9}} + {1 \over {6k – 9 – {k^2}}} + {1 \over {{k^2} + 6k + 9}} \cr & \,\,\,\,\, = {k \over {\left( {k – 3} \right)\left( {k + 3} \right)}} + {{ – 1} \over {{{\left( {k – 3} \right)}^2}}} + {1 \over {{{\left( {k + 3} \right)}^2}}} \cr & \,\,\,\,\, = {{k\left( {k – 3} \right)\left( {k + 3} \right)} \over {{{\left( {k – 3} \right)}^2}{{\left( {k + 3} \right)}^2}}} + {{ – {{\left( {k + 3} \right)}^2}} \over {{{\left( {k – 3} \right)}^2}{{\left( {k + 3} \right)}^2}}} + {{{{\left( {k – 3} \right)}^2}} \over {{{\left( {k – 3} \right)}^2}{{\left( {k + 3} \right)}^2}}} \cr & \,\,\,\,\, = {{k\left( {{k^2} – 9} \right) – \left( {{k^2} + 6k + 9} \right) + \left( {{k^2} – 6k + 9} \right)} \over {{{\left( {k – 3} \right)}^2}{{\left( {k + 3} \right)}^2}}} \cr & \,\,\,\,\, = {{{k^3} – 9k – {k^2} – 6k – 9 + {k^2} – 6k + 9} \over {{{\left( {k – 3} \right)}^2}{{\left( {k + 3} \right)}^2}}} \cr & \,\,\,\,\, = {{{k^3} – 21k} \over {{{\left( {k – 3} \right)}^2}{{\left( {k + 3} \right)}^2}}} \cr} \)