We'll multiply the by
x.
xx+8
x⋅x(x+8)⋅x
x⋅xx⋅x+8⋅x
x2x2+8x
We have squared
x in both the numerator and denominator. These terms can never be negative but how about the term
8x? Yes, if
x is negative. Thus, if
x2−8x<0 the whole expression will be negative. Lets' try with the smallest negative integer,
x=-1. x2x2+8x
(-1)2(-1)2+8(-1)
Simplify power and product
11−8
1-7
-7
Therefore, Ron-Jon is incorrect as we found a negative value.