# Simplifying a rational expression

1. Aug 17, 2015

### Mr Davis 97

Given that we have the expression $\displaystyle-\frac{1}{(x-2)(x-2)(x-3)}~\cdot~\sqrt{\frac{(x-2)^{2}}{(x-3)(x-1)}}$, how do we simplify it, step by step? Specifically, I am concerned about the $\sqrt{(x-2)^{2}}$ term. Are we allowed to cancel this with the $(x-2)$ in the denominator?

2. Aug 17, 2015

### paisiello2

Yes.

3. Aug 17, 2015

### jbriggs444

I disagree. You have to be careful about signs. The square root of x squared is not always equal to x.

Take, for instance, x=0 and evaluate the given expression before and after cancellation. Do the two give the same result?

4. Aug 17, 2015

### Staff: Mentor

I agree with jbriggs444 here, and would add that $\sqrt{x^2} = |x|$, which is something I mentioned in your other thread on rational expressions.

5. Aug 18, 2015

### HallsofIvy

By the way- this is not a "rational function"!