若x，y都是实数，且满足y＜x−1+1−x+12，化简：|1−y|y−1．

Question

若x，y都是实数，且满足y＜√(x−1)+√(1−x)+(1)/(2)，化简：(|1−y|)/(y−1)．

Answer 1

依题意，有

x−1≥0

1−x≥0

，得x=1，此时y＜(1)/(2)，
所以1-y＞(1)/(2)＞0，
所以(|1−y|)/(y−1)＝(1−y)/(y−1)=-1．