Question

简化代数式(x²-1)/(x²+2x)÷(x-1)/x,并判断当x满足不等式组x+2-6时该代数式的符号

Answer 1

x2-1 x2+2x ÷x-1 x

=x2-1 x2+2x •x x-1

=(x -1)(x+1) x(x +2) •x x-1

=x+1 x+2 ,

x+2＜1① 2(x-1)＞-6② ,

解不等式①,得x＜-1．

解不等式②,得x＞-2．

所以,不等式组 x+2＜1 2(x-1)＞-6 的解集是-2＜x＜-1．

当-2＜x＜-1时,x+1＜0,x+2＞0,

所以x+1 x+2 ＜0,即该代数式的符号为负号． 能看懂么,