Originally Posted by

**querti09** This is a system of inequations for which I want to find the set of answers.

$\displaystyle (x-1)(x+2)<(x+2)(x-3)$

$\displaystyle (x+3)(x+5)>(x+4)(x+3)$

What I CAN'T do here is the following:

We start with the first inequation $\displaystyle (x-1)(x+2)<(x+2)(x-3)$

1) I divide both sides of the inequation by $\displaystyle (x+2)$

and I get:

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

2) I cancel the $\displaystyle (x+2)$

in top and bottom of both members of the inequality and I get:

$\displaystyle (x-1)<(x-3)$

In other words:

$\displaystyle x-1<x-3$

Then solving this inequality I get:

3) $\displaystyle 0<-2$

And this is plainly wrong: Then my question is WHY, what's wrong with this procedure.

I know the right one so I don't need the correct procedure, but instead what I'm looking for is an explanation about how come this is incorrect (not just saying because the answer is wrong, I know the correct answer) I thought that perhaps has to do with order of operations...