Question

先化简，再求值：m-m²/m²-1÷m/m-1·(m+1/m-1)²，其中m=2.

Answer 1

原式=-m(m-1)/(m+1)(m-1)×(m-1)/m×(m+1)²/(m-1)²
=-m/(m+1)×(m-1)/m×(m+1)²/(m-1)²
=-(m-1)/(m+1)×(m+1)²/(m-1)²
=-(m+1)/(m-1)
=-(2+1)/(2-1)
=-3

Answer 2

当m=2时
原式=[-(m-1)m(m-1)/(m-1)(m+1)m](m+1/m-1)²
==[-(m-1)/(m+1)](m+1/m-1)²
=-(m+1)/(m-1)
=-3/(2-1)
=-3

Answer 3

m(1-m) (m-1) (m+1)² / (m+1)(m-1)(m-1)(m-1)²
=- m(m+1) / (m-1)(m-1)

代入m=2
= -6 / 1
= -6

Answer 4

解：
原式=-m(m-1)/(m+1)(m-1)×(m-1)/m×(m+1)²/(m-1)²
=-m/(m+1)×(m-1)/m×(m+1)²/(m-1)²
=-(m-1)/(m+1)×(m+1)²/(m-1)²
=-(m+1)/(m-1)
=-(2+1)/(2-1)
=-3

Answer 5

原式=(1-m)/(m+1) * (m+1)²/(m-1)² （把m-m²换成m(1-m)，再用平方差公式）
=-1 * (m+1)/(m-1) （(1-m)=-(m-1)）
=-1 * (2+1)/(2-1)
=-3