Canceling with Variables
Variables can be canceled in fractions just as whole numbers can be.
Examples
When you see
a plus or minus sign in a fraction, be very careful when you
cancel. For
example in the expression 
, x cannot be canceled. The only
quantities
that can be canceled are factors. Many students mistakenly ‘‘cancel’’
the x and
conclude that 
. These equations
are false.
If were equal to 2 or to 3, then we could
substitute any value
for x (except
for 0) and we would get a true equation. Let’s try x = 19: 
.
We can see
that 
. The reason that the x cannot be
factored is
that x is a term in this expression, not a factor. (A term is a
quantity
separated from others by a plus or minus sign.) If you must cancel
the x out of , you must rewrite the fraction:
Simply
because a plus or minus sign appears in a fraction does not automatically
mean that
canceling is not appropriate. For instance 
because any nonzero quantity
divided by itself is one.
Examples
The reason 2
+ 3x can be canceled is that 2 + 3x is a factor of
(2 + 3x)(x –
1).
Practice
Solutions
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