12/（4x²-1）+1=2x+3/1-2x

12/（4x²-1）+1=2x+3/1-2x

12/(2x+1)(2x-1)+1=-(2x+3)/(2x-1)
Multiply by (2x + 1) (x-1)
12+4x²-1=-4x²-8x-3
8x²+8x+14=0
The discriminant is less than 0
unsolvable

420/x+20=420/x-0.5
Is it necessary to multiply both sides of the equation by X (x + 0.5)
Can we split the left one first?
Now I don't know when to use the basic properties of fractions or equations

Is to multiply both sides of the equation by X (x-0.5)
420(x-0.5)+20x（x-0.5）=420X
-210+20X*X-10X=0
X1=-3 X2=7/2

Solving fractional equation
（1）（2x²+1）\（x+2）=2x
（2）（x-2）\（x+2）-1=3\（x²-4）
（3） 3\（x-2 ）+x\（2-x） = -2

One
（2x²+1）\（x+2）=2x
（2x²+1）\（x+2）-2x=0
（2x²+1）\（x+2）-2x （x+2）\ （x+2）=0
(2x²+1-2x²-4x)/(x+2)=0
(1-4x)/(x+2)=0
1-4x=0
x=1/4
two
（x-2）\（x+2）-1=3\（x²-4）
((x-2)(x-2))/((x+2)(x-2))-1=3/(x²-4)
(x²-4x+4)/(x²-4)-1=3/(x²-4)
(x²-4x+4)-(x²-4)=3
x²-4x+4-x²+4=3
-4x+8=3
-4x=-5
x=5/4
three
3\（x-2 ）+x\（2-x） = -2
3/(x-2)+x/-(x-2)=-2
3/(x-2)-x/(x-2)=-2
(3-x)/(x-2)=-2
3-x=-2(x-2)
3-x=-2x+4
x=1