1.解不等式(2-4X)/(X²-3x+2)≥X+1
两边同乘以-1,得(4x-2)/(x²-3x+2)≦-(x+1)
移项通分得[(4x-2)+(x+1)(x²-3x+2)]/(x²-3x+2)=x(x²-2x+3)/(x-1)(x-2)≦0
由于x²-2x+3=(x-1)²+2≧2>0,故可将其去掉得到同解不等式：x/(x-1)(x-2)≦0
于是用根轴法很快得到其解集为:{x︱x≦0}∪{x︱1
几道高一第一学期的数学题,解不等式一题,基本不等式一题,不等式证明一题求值域一题,
1.解不等式(2-4X)/(X²-3x+2)≥X+1
两边同乘以-1,得(4x-2)/(x²-3x+2)≦-(x+1)
移项通分得[(4x-2)+(x+1)(x²-3x+2)]/(x²-3x+2)=x(x²-2x+3)/(x-1)(x-2)≦0
由于x²-2x+3=(x-1)²+2≧2>0,故可将其去掉得到同解不等式：x/(x-1)(x-2)≦0
于是用根轴法很快得到其解集为:{x︱x≦0}∪{x︱1