Question

Rezolvați ecuațiile:
a) 2x-1/x+7=3x+4/x-1
b) x-1/x patrat -1=x/6
h)3x+1/x+2=x-1/x-2
j)x-7/3x+1=x/x-3

Answer 1

a) (2x-1)/(x+7)=(3x+4)/(x-1)
(2x-1)(x-1)=(3x+4)(x+7)
2x²-x-2x+1=3x²+4x+21x+28
x²+28x+27=0
x²+27x+x+27=0
x(x+27)+(x+27)=0
(x+27)(x+1)=0
x=-27
x=-1

b)( x-1)/(x² -1)=x/6
1/(x +1)=x/6
x²+x-6=0
x²-2x+3x-6=0
x(x-2)+3(x-2)=0
(x-2)(x+3)=0
x=2
x=-3

h)(3x+1)/(x+2)=(x-1)/(x-2)
(3x+1)(x-2)=(x+2)/(x-1)
3x²+x-6x-2=x²+2x-x-2
2x²-6x=0
2x(x-3)=0
x=0
x=3

j)(x-7)/(3x+1)=x/(x-3)
(x-7)(x-2)=x(3x+1)
x²-7x-2x+14=3x+3
x²-12x+11=0
x²-11x-x+11=0
x(x-11)-(x-11)=0
(x-11)(x-1)=0
x=11
x=1