Toán Lớp 8: x/x-y+y/x+y+2y^2/x^2-y^2 cộng các phân thức
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Toán Lớp 8: x/x-y+y/x+y+2y^2/x^2-y^2 cộng các phân thức
Comments ( 2 )
Giải đáp:
= {x + y}/{x – y}
Lời giải và giải thích chi tiết:
x/{x – y} + y/{x + y} + {2y^2}/{x^2 – y^2} (ĐKXĐ: x ne – y ; x ne y)
= x/{x – y} + y/{x + y} + {2y^2}/{(x – y)(x + y)}
= {x(x + y)}/{(x – y)(x + y)} + {y(x – y)}/{(x – y)(x + y)} + {2y^2}/{(x – y)(x + y)}
= {x^2 + xy}/{(x – y)(x + y)} + {xy – y^2}/{(x – y)(x + y)} + {2y^2}/{(x – y)(x + y)}
= {x^2 + xy + xy – y^2 + 2y^2}/{(x – y)(x + y)}
= {x^2 + (xy + xy) + (2y^2 – y^2)}/{(x – y)(x + y)}
= {x^2 + 2xy + y^2}/{(x – y)(x + y)}
= {(x + y)^2}/{(x – y)(x + y)}
= {x + y}/{x – y}
Giải đáp:
x/(x – y) + y/(x + y) + (2y^2)/(x^2 – y^2) (x \ne ± y)
= x/(x – y) + y/(x + y) + (2y^2)/[(x – y).(x + y)]
= [x.(x + y)]/[(x – y).(x + y)] + [y.(x – y)]/[(x – y).(x + y)] + (2y^2)/[(x – y).(x + y)]
= [x^2 + xy]/[(x – y).(x + y)] + [xy – y^2]/[(x – y).(x + y)] + (2y^2)/[(x – y).(x + y)]
= [x^2 + xy + xy – y^2 + 2y^2)/[(x – y).(x + y)]
= [x^2 + 2xy +y^2]/[(x – y).(x + y)]
= [(x + y)^2]/[(x – y).(x + y)]
= [x + y]/[x – y]
$#dairana$