Question

Решить дробно рациональное уравнение.
1. x+1/6+20/x-1=4
2. 12/x-1 - 8/x+1=2
3. 16/x-3+30/1-x=3

Answer 1

1
x≠1
(x+1)(x-1)+20*6=4*6(x-1)
x²-1+120-24x+24=0
x²-24x+143=0
x1+x2=24 U x1*x2=143
x1=11 U x2=13
2
x≠1,x≠-1
12(x+1)-8(x-1)=2(x²-1)
2x²-2-12x-12+8x-8=0
2x²-4x-22=0
x²-2x-11=0
D=4+44=48
x1=(2-4√3)/2=1-2√3
x2=1+2√3
3
x≠3,x≠1
16(1-x)+30(x-3)=3(x-3)(1-x)
16-16x+30x-90-3x+3x²+9-9x=0
3x²+2x-65=0
D=4+780=784
x1=(-2-28)/6=-5
x2=(-2+28)/6=13/3