Question

x-3÷x+1 - x+1÷ x-2 = 1 aftati x

Answer 1

(x-3)/(x+1)-(x+1)/(x-2)=1/x
[(x-3)(x-2)-(x+1)(x+1)]/(x+1)(x-2)=1/x
[x²-2x-3x+6-x²-2x-1]/(x²-x-2)=1/x
(-7x+5)/(x²-x-2)=1/x
x(-7x+5)=x²-x-2
-7x²+5x=x²-x-2
-7x²-x²+5x+x+2=0
-8x²+6x+2=0                  ·(-1)
8x²-6x-2=0                       :2
4x²-3x-1=0
Δ=9+16=25
x₁=(3+5)/8=8/8
x₁=1
x2=(3-5)/8=-2/8=-1/4
x₂=-1/4
x∈{-1/4, 1}