Solving inequality with fractions 1/(x-1) + 2/(x-2) - 3/(x-3) < 0

[Brunno]

I got to the solution!

$$\frac{1}{x-1}+\frac{2}{x-2}-\frac{3}{x-3}$$<0

$$\frac{1(x-2)(x-3)+2(x-1)(x-3)-3(x-1)(x-2)}{(x-1)(x-2)(x-3)}$$

(x-2)(x-3)=x²-3x-2x+6

(2x-2(x-3)=2x²-6x-2x+6=2x²-8x+6

-3x+3(x-2)=-3x²+6x+3x+6=-3x²+9x-6$$\frac{-4x+6}{(x-1)(x-2)(x-3)}$$

-4x+6<0 --> -4x<-6 --> x>3/2

x-1>0 --> x>1

x-2>0 --> x>2

x-3>0 --> x>3

S={x E R/x<1 or 3/2<x<2 or x>3}

So guys,I thank you all very much to show that i could do this by myself!

Now I believe "Yes we can".

 

[Mark44]

Good job!