Tìm phân thức P biết :
a. \(P:{{4{x^2} - 16} \over {2x + 1}} = {{4{x^2} + 4x + 1} \over {x - 2}}\)
b. \({{2{x^2} + 4x + 8} \over {{x^3} - 3{x^2} - x + 3}}:P = {{{x^3} - 8} \over {\left( {x + 1} \right)\left( {x - 3} \right)}}\)
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a. \(P:{{4{x^2} - 16} \over {2x + 1}} = {{4{x^2} + 4x + 1} \over {x - 2}}\)
\(\eqalign{ & \Rightarrow P = {{4{x^2} - 16} \over {2x + 1}}.{{4{x^2} + 4x + 1} \over {x - 2}} = {{4\left( {x + 2} \right)\left( {x - 2} \right)} \over {2x + 1}}.{{{{\left( {2x + 1} \right)}^2}} \over {x - 2}} \cr & P = 4\left( {x + 2} \right)\left( {2x + 1} \right) = 4\left( {2{x^2} + x + 4x + 2} \right) = 8{x^2} + 40x + 8 \cr} \)
b. \({{2{x^2} + 4x + 8} \over {{x^3} - 3{x^2} - x + 3}}:P = {{{x^3} - 8} \over {\left( {x + 1} \right)\left( {x - 3} \right)}}\)
\(\eqalign{ & \Rightarrow P = {{2{x^2} + 4x + 8} \over {{x^3} - 3{x^2} - x + 3}}:{{{x^3} - 8} \over {\left( {x + 1} \right)\left( {x - 3} \right)}} \cr & P = {{2\left( {{x^2} + 2x + 4} \right)} \over {\left( {x - 3} \right)\left( {x + 1} \right)\left( {x - 1} \right)}}.{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right)}} = {2 \over {\left( {x + 1} \right)\left( {x - 2} \right)}} = {2 \over {{x^2} - x - 2}} \cr} \)