大师作文网计算：x/x-y+y/x+y-2xy/x²-y².先化简,再求值：a+1/a-1-a/a²
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/17 21:57:29
计算：x/x-y+y/x+y-2xy/x²-y².先化简,再求值：a+1/a-1-a/a²-2a+1÷1/a,其中a=1-根号2 若1/x+1/y=2,求2x-xy+2y/3x+5xy+3y的值.
1、原式=x/(x-y)+y/(x+y)-2xy/(x+y)(x-y)
=x(x+y)/(x+y)(x-y)+y(x-y)/(x+y)(x-y)-2xy/(x+y)(x-y)
=(x^2+xy+xy-y^2-2xy)/(x+y)(x-y)
=(x+y)(x-y)/(x+y)(x-y)
=1
2、化简所求式=(a+1)/(a-1)-a/(a-1)^2÷1/a
=(a+1)/(a-1)-a^2/(a-1)^2
=(a+1)(a-1)/(a-1)^2-a^2/(a-1)^2
=(a^2-1-a^2)/(a-1)^2
=-1/(a-1)^2
当a=1-√2时,所求式=-1/(1-√2-1)^2
=-1/2
3、（内个,所求式是不是(2x-xy+2y)/(3x+5xy+3y)）
所求式=(2/y-1+2/x)/(3/y+5+3/x)（分子分母同时除以xy）
=[2(1/x+1/y)-1]/[3(1/x+1/y)+5]
=(2×2-1)/(3×2+5)
=3/11
=x(x+y)/(x+y)(x-y)+y(x-y)/(x+y)(x-y)-2xy/(x+y)(x-y)
=(x^2+xy+xy-y^2-2xy)/(x+y)(x-y)
=(x+y)(x-y)/(x+y)(x-y)
=1
2、化简所求式=(a+1)/(a-1)-a/(a-1)^2÷1/a
=(a+1)/(a-1)-a^2/(a-1)^2
=(a+1)(a-1)/(a-1)^2-a^2/(a-1)^2
=(a^2-1-a^2)/(a-1)^2
=-1/(a-1)^2
当a=1-√2时,所求式=-1/(1-√2-1)^2
=-1/2
3、（内个,所求式是不是(2x-xy+2y)/(3x+5xy+3y)）
所求式=(2/y-1+2/x)/(3/y+5+3/x)（分子分母同时除以xy）
=[2(1/x+1/y)-1]/[3(1/x+1/y)+5]
=(2×2-1)/(3×2+5)
=3/11
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