Bài 1. Thực hiện phép tính:
a) \(a:\left( {a + {1 \over a}} \right)\)
b) \(\left( {{a \over b} + {b \over a} – 2} \right):\left( {{1 \over b} – {1 \over a}} \right).\)
Bài 2. Tìm P, biết: \({{x – y} \over {{x^3} + {y^3}}}.P = {{{x^2} – 2xy + {y^2}} \over {{x^2} – xy + {y^2}}}.\)
Bài 3. Rút gọn: \(Q = \left( {{{{a^2}} \over {a + b}} – {{{a^3}} \over {{a^2} + 2ab + {b^2}}}} \right):\left( {{a \over {a + b}} – {{{a^2}} \over {{a^2} – {b^2}}}} \right).\)
Bài 1. a) \(a:\left( {a + {1 \over a}} \right) = a:{{{a^2} + 1} \over a} \)
Advertisements (Quảng cáo)
\(\;= a.{a \over {{a^2} + 1}} = {{{a^2}} \over {{a^2} + 1}}.\)
b) \(\left( {{a \over b} + {b \over a} – 2} \right):\left( {{1 \over b} – {1 \over a}} \right) \)
\(\;= {{{a^2} + {b^2} – 2ab} \over {ab}}:{{a – b} \over {ab}}\)
\(\;= {{{{\left( {a – b} \right)}^2}} \over {ab}}.{{ab} \over {a – b}} = a – b.\)
Advertisements (Quảng cáo)
Bài 2. \(P = {{{{\left( {x – y} \right)}^2}} \over {{x^2} – xy + {y^2}}}:{{x – y} \over {{x^3} + {y^3}}}\)
\(\;\;\;\;= {{{{\left( {x – y} \right)}^2}} \over {{x^2} – xy + {y^2}}}.{{{x^3} + {y^3}} \over {x – y}}\)
\(\;\;\;\; = \left( {x – y} \right)\left( {x + y} \right) = {x^2} – {y^2}.\)
Bài 3. \(Q = {{{a^2}\left( {a + b} \right) – {a^3}} \over {{{\left( {a + b} \right)}^2}}}:{{a\left( {a – b} \right) – {a^2}} \over {{a^2} – {b^2}}}\)
\(\;\;\;\;= {{{a^2}b} \over {{{\left( {a + b} \right)}^2}}}.{{{a^2} – {b^2}} \over { – ab}} = – {{a\left( {a – b} \right)} \over {a + b}} = {{ab – {a^2}} \over {a + b}}.\)
