求间算1/(x-5y)－1/(x-6y)－1/(x-8y)＋1/(x-9y)=
1人问答
问题描述：
求间算1/(x-5y)－1/(x-6y)－1/(x-8y)＋1/(x-9y)=
田新华回答：
1/(x-5y)－1/(x-6y)－1/(x-8y)＋1/(x-9y)
=1/(x-5y)－1/(x-8y)＋1/(x-9y)－1/(x-6y)
=[(x-8y)-(x-5y)]/[(x-5y)(x-8y)]+[(x-6y)-(x-9y)]/[(x-9y)(x-6y)]
=(-3y)/[(x-5y)(x-8y)]+3y/[(x-9y)(x-6y)]
=3y*{1/[(x-9y)(x-6y)]-1/[(x-5y)(x-8y)]}
=3y*[(x-5y)(x-8y)-(x-9y)x-6y)]/[(x-9y)(x-6y)(x-5y)(x-8y)]
=3y*[(x²-13xy+40y²)-(x²-15xy+54y²)]/[(x-9y)(x-6y)(x-5y)(x-8y)]
=3y*(2xy-14y²)/[(x-9y)(x-6y)(x-5y)(x-8y)]
=6y²(x-7y)/[(x-9y)(x-6y)(x-5y)(x-8y)]
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