Perform and Simplify.
x/x-y - 2y^2/x^2 -y^2
Math homework. Perform and Simplify.?
2009-03-11 11:51 am
回答 (2)
2009-03-11 12:10 pm
✔ 最佳答案
....x..........2y^2--------- - -------------
....x-y....(x+y)(x-y)
...x(x+y)-2y^2
=-------------------
...(x+y)(x-y)
. x^2+xy-2y^2
=------------------
...(x+y)(x-y)
..(x+2y)(x-y)
=-----------------
...(x+y)(x-y)
..x+2y
=--------- answer//
..x+y
2009-03-11 12:26 pm
x/(x - y) - (2y^2)/(x^2 - y^2)
= [x(x + y)]/[(x + y)(x - y)] - (2y^2)/[(x + y)(x - y)]
= (x^2 + xy - 2y^2)/[(x + y)(x - y)]
= [x^2 + 2xy - xy - 2y^2]/[(x + y)(x - y)]
= [(x^2 + 2xy) - (xy + 2y^2)]/[(x + y)(x - y)]
= [x(x + 2y) - y(x + 2y)]/[(x + y)(x - y)]
= [(x + 2y)(x - y)]/[(x + y)(x - y)]
= (x + 2y)/(x + y)
= [x(x + y)]/[(x + y)(x - y)] - (2y^2)/[(x + y)(x - y)]
= (x^2 + xy - 2y^2)/[(x + y)(x - y)]
= [x^2 + 2xy - xy - 2y^2]/[(x + y)(x - y)]
= [(x^2 + 2xy) - (xy + 2y^2)]/[(x + y)(x - y)]
= [x(x + 2y) - y(x + 2y)]/[(x + y)(x - y)]
= [(x + 2y)(x - y)]/[(x + y)(x - y)]
= (x + 2y)/(x + y)
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