Question

化简((a^2-1)/(a^2-5a+6))/((a^2+a-2)/(a-3))-(a+3)/(a^2-4),其中=-3

Answer 1

((a^2-1)/(a^2-5a+6))/((a^2+a-2)/(a-3))-(a+3)/(a^2-4)
= ((a^2-1)/(a^2-5a+6)) * ((a-3)/(a^2+a-2)) - (a+3)/(a^2-4)
= [(a-1)(a+1)] / [(a-2)(a-3)] * (a-3)/[(a-1)(a+2)] - (a+3)/[(a-2)(a+2)]
= (a+1) / (a-2) * 1/(a+2) - (a+3)/[(a-2)(a+2)]
= (a+1) / [(a-2)(a+2)] - (a+3)/[(a-2)(a+2)]
= [(a+1) - (a+3)] / [(a-2)(a+2)]
= (-2) / [(a-2)(a+2)]
= (-2) / (a^2 - 4)

若 a=-3
上式 = (-2)/(9-4) = -2/5

追问

只是初二的题，还是初三的

Answer 2

((a^2-1)/(a^2-5a+6))/((a^2+a-2)/(a-3))-(a+3)/(a^2-4)
= ((a^2-1)(a-3))/((a^2-5a+6) * (a^2+a-2)) - (a+3)/(a^2-4)
= [(a-1)(a+1)(a-3)] / [(a-2)(a-3) * (a-1)(a+2)] - (a+3)/(a^2-4)
= (a+1) / (a^2-4)] - (a+3)/(a^2-4)
= -2/ (a^2 - 4)
若 a=-3
上式 = (-2)/(9-4) = -2/5