## Introductory Algebra for College Students (7th Edition)

If you multiply the second expression with $-1$, you have changed the problem. For instance, you want to add $A+B$ and multiply B with -1, you get $A+(-B)=A-B$, which is not equivalent to the problem you started out with. What you want instead, is to multiply B with $1.$ It doesn't change then. When B is a rational expression, you multiply with $\displaystyle \frac{-1}{-1}$, which is 1. In this way you multiply BOTH the numerator and denominator with -1, but you don't change the value of the expression. Doesn't make sense.