Question

Is this correct?

Answer 1

No, in order to have factors in the numerator and denominator cancel, you must have those factors in both the numerator and denominator.

For example:
\[\frac{x^2}{xy}=\frac{x\times x}{xy}=\frac{\cancel{x}\times x}{\cancel{x}y}=\frac{x}{y}\]

Answer 2

if you have the same letter "up top" and "down below" they "cancel"
i.e. anything divided by itself is 1.

for numbers, if the top and bottom number can both be divided by the same number, you can simplify
notice in the last choice 4 up top and 16 down below: both are divisible by 4 (and by 2), so you can simplify

Answer 3

even more tricky: x^2+6x+9 = (x+3)(x+3)
and (x+3) is in the top (twice) and once in the bottom. so you can cancel (x+3)/(x+3)
(leaving just one (x+3) up top and none in the bottom)

Answer 4

I understand now. Thanks!