I solved this question that way

But the answer in the solution manual is

I don't understand why they made it -x in the denominator

xvxvxv
Oct 7, 2014

#1**+13 **

The original form of the denominator shows it is positive for all values of x (even when x is negative). Therefore, if you take x outside the square root sign, you must still keep the denominator positive, so if x is negative you must have -x, instead of just x, to keep it positive.

To convince yourself that this is the right thing to do look at the following graph:

Alan
Oct 7, 2014

#1**+13 **

Best Answer

The original form of the denominator shows it is positive for all values of x (even when x is negative). Therefore, if you take x outside the square root sign, you must still keep the denominator positive, so if x is negative you must have -x, instead of just x, to keep it positive.

To convince yourself that this is the right thing to do look at the following graph:

Alan
Oct 7, 2014