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 expres
, x cannot be canceled. The only quantities that can
be canceled are factors. Many students mistakenly ‘‘cancel’’ the x and
conclude that
or
. 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
and
. 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.
Practice
Solutions
Sumber
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