bài 1:
a,A = (x/x+2 + 6/x-2 - 2x+12/x^2-4):(2x-3/x+1 - 1)
=[x(x-2)/(x+2).(x-2) + 6(x+2)/(x+2).(x-2) - 2x+12/(x+2).(x-2)] : [2x-3-(x+1)/x+1]
= [x^2-2x+6x+12-2x-12/(x+2).(x-2) ] : (2x-3-x-1/x+1)
=x^2+2x/(x+2).(x-2) : (x-4)/x+1
=[x(x+2)/(x+2).(x-2) ] . (x+1/x-4)
=x/x-2 . x+1/x-4
=x(x+1)/(x-2)(x-4)
=x^2+x/x^2-6x+8
b, thay x=4 vào A ta có :
A=4^2+4/4^2-6.4+8=16+4/16-24+8=0
c, A=-3/4 =>x^2+x/x^2-6x+8=-3/4<=>4(x^2+x)=-3(x^2-6x+8)<=>4x^2+4x=-3x^2+18x-24<=>4x^2+4x+3x^2-18x+24=0<=>x^2-14x+24=0<=>x^2-2x-12x+24=0<=>(x-2).(x-12)=0<=>x=2 hoặc x=12