How to solve? x^2-4x+3 ________

First we can factor into

(x -
3)(x - 1)/sqrt((2-x)(1+x)) < 0

The sqrt is by
definition positive so we have to check when (x - 3)(x - 1) <
0

We have two cases

x - 3
< 0 and x - 1 > 0  this gives us 1 < x <
3

x - 3 > 0 and x - 1 < 0 this gives x
< 1 and x > 3 there is no solution to
this.

The only other condition is (2-x)(1+x) >
0

We again have two cases because the argument to square
root must be positive

2 - x > 0 and 1 + x > 0
this gives us x < 2 and x > -1 which means -1 < x <
2.

2 - x < 0 and 1 + x < 0 this gives us x
> 2 and x < -1 which has no
solution

Combining this with our previous result that 1
< x < 3 and -1 < x <
2

we get the solution 1 < x <
2. or x is an element of (1, 2)