Question

先化简，再求值:(1/(x+y)+2/(x^2-xy))÷(x+2)/2x，其中实数x、y满足y=√(x-2)-√(4-2x)+1

Answer 1

根号下大于等于0
所以x-2≥0且4-2x≥0
x≥2且x≤2
同时满足则x=2
y=0-0+1=1

所以原式=[1/(x+y)+2/x(x-y)]÷(x+2)/2x
=[x(x-y)+2(x+y)]/x(x+y)(x-y)÷(x+2)/2x
=(x²-xy+2x+2y)/x(x+y)(x-y)×2x/(x+2)
=2(x²-xy+2x+2y)/(x+y)(x-y)(x+2)
=2(4-2+4+2)/(2+1)(2-1)(2+2)
=16/12
=4/3