Simplifying a rational expression

[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?

 

[paisiello2]

Yes.

 

[jbriggs444]

Yes.

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?

 

[Mark44]

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?

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.

 

[HallsofIvy]

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