Question

化简,求值:m2-1/m2-2m+1÷(m-1-m+1/m-1),其中m=√3

Answer 1

(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

Answer 2

m2-1/m2-2m+1÷(m-1-m+1/m-1),其中m=√3
=(m+1)(m-1)/(m-1)^2 ÷(((m-1)^2-m+1)/m-1)
=(m+1)/(m-1) *(m-1)/(m^2-2m+1-m+1)
=(m+1)/(m^2-3m+2)
=(m+1)/(m-2)(m-1)
=(√3+1)/(√3-2)(√3-1)
=(√3+1)^2/(√3-2)(√3-1)(√3+1)
=(3+2√3+1)/(√3-2)(3-1)
=2(2+√3)/2(√3-2)
=(2+√3)/(√3-2)
=(√3+2)^2/(√3-2)(√3+2)
=(3+2√3+4)/(3-4)
=-7-2√3