Question

1. ((X+3)/(x-3)) + ((x-3)/(x+3)) = 10/3 2. ((X+1)/(x-1)) + ((x-1)/(x+1)) = 2.1/2

Answer 1

1.    х+3/х-3=t    ⇒t+1/t=10/3⇒t^2+1=10/3*t
3t^2-10t+3=0    D=100-36=64  √64=8
t1=1/6*(10+8)=3     t2=1/6*(10-8)=1/3

t=3   x+3/x-3=3   x+3=3x-9  2x=12   x=6
t=1/3   x+3=1/3*x-1  2/3x=-4   x=-4*3/2=-6

2.  x+1/x-1=t   t+1/t=5/2   t^2-5/2·t+1=0⇒2t^2-5t+2=0
D=25-4*2*2=9   √9=3
t1=1/4*(5+3)=2      t2=1/4*(5-3)=1/2
t=2    x+1/x-1=2   x+1=2x-2   x=3
t=1/2   x+1=0.5x-0.5   0.5x=-3/2    x=-3