已知实数x,y满足x+y+1大于等于0且2x-y+2大于等于0且x小于等于0,则(x+y)\(x+1)的取值范围

已知实数x,y满足x+y+1大于等于0且2x-y+2大于等于0且x小于等于0,则(x+y)\(x+1)的取值范围
已知实数x,y满足x+y+1大于等于0且2x-y+2大于等于0且x小于等于0,则(x+y)\(x+1)的取值范围

已知实数x,y满足x+y+1大于等于0且2x-y+2大于等于0且x小于等于0,则(x+y)\(x+1)的取值范围
不等式推论：
x+y+1≥0 ===> x+y ≥ -1 y ≥ -x-1
2x-y+2≥0 ===> 2x+2 ≥ y x+1 ≥ y/2 ≥ -1/2 且x≤0 ==> -3/2≤x≤0 ==>
①当x∈[-3/2,-1)时,1/(x+1)∈(-∞,-2]
②当x∈(-1,0]时,1/(x+1)∈[1,+∞)
③x=-1时为间断点.
④ -1≤ -x-1 ≤1/2 ==> y ≥1/2
(1)讨论当y=1/2时,x+y = x+1/2 ∈ [-1,1/2]
(x+y)/(x+1) 的取值范围讨论：
① 当x∈[-3/2,-1)时,(x+y)= x+1/2 ∈ [-1,-1/2] ===> (x+y)/(x+1) ∈ [+2,+∞)
②当x∈(-1,0]时,(x+y)= x+1/2 ∈ [-1/2,1/2] ===> (x+y)/(x+1)∈(-∞,+1/2]
③x=-1时为间断点.
(2)同理,当y > 1/2时,可以推论(x+y)/(x+1) 的取值范围,这个留给你自行推论.