2/(2x-3)+3/(x-1)=6/(2x²-5x+3)-1 ОДЗ: 2x-3≠0 х≠1,5 x-1≠0 x≠1
2/(2*(x-1,5)+3/(x-1)=6/(2*(x-1)(x-1,5))
2*(x-1)+3*2*(x-1,5)=6-1*(2*(x-1)(x-1,5))
2x-2+6x-9=6-2x²+5x-3
2x²+3x-14=0 D=121
x₁=2 x₂=-3,5.
Ответ: х₁=2 х₂=-3,5.
14/(x²-9)+1/(3-x)+(4-x)/(x+3)-7/(x+3)=0 ОДЗ: х≠+/-3.
14/((x-3)(x+3))-1/(x-3)+(4-x-7)/(x+3)=0
14/((x-3)(x+3))-1/(x+3)-(x+3)/(x+3)=0
14/((x-3)(x+3))-1/(x-3)-1=0
14-1*(x+3)-x²+9=0
14-x-3-x²+9=0
x²+x-20=0 D=81
x₁=4 x₂=-5
Ответ: х₁=4 х₂=-5.