Question

Resolva a equaçao. b) (ufmg) 2/×-1 + 1/ ×-2 = 2

Answer 1

2/×-1 + 1/ ×-2 = 2 ==> *(x-1)(x-2) mmc

2(x-2) + 1(x-1) = 2(x-1)(x-2)

2x-4 + x-1 = 2(x²-3x+2)

3x -5 = 2x²-6x+4

2x² -6x +4 - 3x + 5 = 0

2x² -9x +9 = 0

∆= 81-72= 9 ==> √∆=3

x = 9±3/4

x' = 9+3/4 = 3 ✓

x" = 9-3/4 = 3/2 ✓