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计算:{[-1/6x^(2n+1)y^(2n+1)+1/3x^(2n+1)y(^(2n-1)+1/2x^(2n-1)y^(2n-1)]}/[-1/12x^(2n-1)y^(2n-1)]
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答案和解析
（提公因式）
-1/6x^(2n+1)y^(2n+1)+1/3x^(2n+1)y(^(2n-1)+1/2x^(2n-1)y^(2n-1)
=-1/6x^(2n-1)y^(2n-1)[x^2y^2+2x^2+3x^(2n-1)]
所以
原式=-1/6x^(2n-1)y^(2n-1)[x^2y^2+2x^2+3x^(2n-1)]/[-1/12x^(2n-1)y^(2n-1)]
=2(x^2y^2-2x^2-3)
-1/6x^(2n+1)y^(2n+1)+1/3x^(2n+1)y(^(2n-1)+1/2x^(2n-1)y^(2n-1)
=-1/6x^(2n-1)y^(2n-1)[x^2y^2+2x^2+3x^(2n-1)]
所以
原式=-1/6x^(2n-1)y^(2n-1)[x^2y^2+2x^2+3x^(2n-1)]/[-1/12x^(2n-1)y^(2n-1)]
=2(x^2y^2-2x^2-3)
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