Cùng những phân thức khác mẫu thức:
Cùng những phân thức khác mẫu thức:
a. ({5 over {6{x^2}y}} + {7 over {12x{y^2}}} + {{11} over {18xy}})
b. ({{4x + 2} over {15{x^3}y}} + {{5y - 3} over {9{x^2}y}} + {{x + 1} over {5x{y^3}}})
c. ({3 over {2x}} + {{3x - 3} over {2x - 1}} + {{2{x^2} + 1} over {4{x^2} - 2x}})
d. ({{{x^3} + 2x} over {{x^3} + 1}} + {{2x} over {{x^2} - x + 1}} + {Một over {x + 1}})
Giải:
a. ({5 over {6{x^2}y}} + {7 over {12x{y^2}}} + {{11} over {18xy}})( = {{30y} over {36{x^2}{y^2}}} + {{21x} over {36{x^2}{y^2}}} + {{22xy} over {36{x^2}{y^2}}} = {{30y + 21x + 22xy} over {36{x^2}{y^2}}})
b. ({{4x + 2} over {15{x^3}y}} + {{5y - 3} over {9{x^2}y}} + {{x + 1} over {5x{y^3}}})
(eqalign{ & = {{3{y^2}left( {4x + 2} right)} over {45{x^3}{y^3}}} + {{5x{y^2}left( {5y - 3} right)} over {45{x^3}{y^3}}} + {{9{x^2}left( {x + 1} right)} over {45{x^3}{y^3}}} cr & = {{12x{y^2} + 6{y^2} + 25x{y^3} - 15x{y^2} + 9{x^3} + 9{x^2}} over {45{x^3}{y^3}}} cr&= {{6{y^2} + 25x{y^3} - 3x{y^2} + 9{x^3} + 9{x^2}} over {45{x^3}{y^3}}} cr} )
c. ({3 over {2x}} + {{3x - 3} over {2x - 1}} + {{2{x^2} + 1} over {4{x^2} - 2x}})
( = {3 over {2x}} + {{3x - 3} over {2x - 1}} + {{2{x^2} + 1} over {2xleft( {2x - 1} right)}})
(eqalign{ & = {{3left( {2x - 1} right)} over {2xleft( {2x - 1} right)}} + {{2xleft( {3x - 3} right)} over {2xleft( {2x - 1} right)}} + {{2{x^2} + 1} over {2xleft( {2x - 1} right)}}cr& = {{6x - 3 + 6{x^2} - 6x + 2{x^2} + 1} over {2xleft( {2x - 1} right)}} cr & = {{8{x^2} - 2} over {2xleft( {2x - 1} right)}} cr&= {{2left( {4{x^2} - 1} right)} over {2xleft( {2x - 1} right)}} = {{left( {2x + 1} right)left( {2x - 1} right)} over {xleft( {2x - 1} right)}} = {{2x + 1} over x} cr} )
d. ({{{x^3} + 2x} over {{x^3} + 1}} + {{2x} over {{x^2} - x + 1}} + {Một over {x + 1}})( = {{{x^3} + 2x} over {left( {x + 1} right)left( {{x^2} - x + 1} right)}} + {{2x} over {{x^2} - x + 1}} + {Một over {x + 1}})
(eqalign{ & = {{{x^3} + 2x} over {left( {x + 1} right)left( {{x^2} - x + 1} right)}} + {{2xleft( {x + 1} right)} over {left( {x + 1} right)left( {{x^2} - x + 1} right)}} + {{{x^2} - x + 1} over {left( {x + 1} right)left( {{x^2} - x + 1} right)}} cr & = {{{x^3} + 2x + 2{x^2} + 2x + {x^2} - x + 1} over {left( {x + 1} right)left( {{x^2} - x + 1} right)}} cr&= {{{x^3} + 3{x^2} + 3x + 1} over {left( {x + 1} right)left( {{x^2} - x + 1} right)}} = {{{{left( {x + 1} right)}^3}} over {left( {x + 1} right)left( {{x^2} - x + 1} right)}} cr & = {{{{left( {x + 1} right)}^2}} over {{x^2} - x + 1}} cr} )
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