化简,求值:m2-1/m2-2m+1÷(m-1-m+1/m-1),其中m=√3
问题描述：
化简,求值:m2-1/m2-2m+1÷(m-1-m+1/m-1),其中m=√3
答
(m²-1)/(m²-2m+1)÷[m-1-(m+1)/(m-1)]
=(m+1)(m-1)/(m-1)²÷[m-1-(m+1)/(m-1)]
=(m+1)/(m-1)÷[(m-1)²-(m+1)]/(m-1)
=(m+1)/[(m-1)²-(m+1)]
=(m+1)/m(m-3)
m=√3
所以原式=(√3+1)/√3(√3-3)=-(2+√3)/3