Question

化简 求值 a+1/2a-1

Answer 1

若a>1/2→2a-1>0，则
a+1/(2a-1)
=(2a-1)/2+1/(2a-1)+1/2
≥2√[(2a-1)/2·1/(2a-1)]+1/2
=(1+2√2)/2，
即(2a-1)/2=1/(2a-1)
→a=(1+√2)/2时，
所求最小值为: (1+2√2)/2.
不存在最大值.

a<1/2→1-2a>0时，
a+1/(2a-1)
=-[(1-2a)/2+1/(1-2a)]+1/2
≤-2√[(1-2a)/2·1/(1-2a)]+1/2
=(1-2√2)/2，
故(1-2a)/2=1/(1-2a)，
即a=(1-√2)/2时，
所求最大值为: (1-2√2)/2，
不存在最小值。

Answer 2

a+1/2a-1

解，原式=1/2（2a-1）+3/2/2a-1
=1/2+3/4a-2

Answer 3

条件确实，至少要知道a的取值！

Answer 4

[(a-1)/(a+2)]×[(a²-4)/(a²-2a+1)]÷[1/(a²-1)]
=(a-1)(a²-4)(a²-1)/[(a+2)(a²-2a+1)]
=(a-1)(a+2)(a-2)(a+1)(a-1)/[(a+2)(a-1)²]
=(a-2)(a+1)
=a²-a-2
=(a²-a-7)+5
=0+5
=5