Simplify the following expression by canceling common factors, if possible:
Answer
Pull out and cancel the common factor 4 for .
Example 2
Simplify the following expression by canceling common factors, if possible:
Answer
Pull out and cancel the common factor 5x for .
Example 3
Simplify the following expression by canceling common factors, if possible:
Answer
The common factor is 11xy. Canceling gives us
Example 4
A student was asked to remove all possible common factors from the following rational expression: . The student wrote: Identify the mistake, if any.
Answer
That numerator is the problem: 3x4 + 6x2 – 3x = 3x(x3 – 2x – 1), not 3x(x2 – 2x). Looks like someone forgot a few terms.
Example 5
A student was asked to remove all possible common factors from the following rational expression: The student wrote: Identify the mistake, if any.
Answer
We're not allowed to cancel the x2 and 2x terms that way. In order to cancel them, common factors must be factors of every term in both the numerator and denominator of the rational expression. Just because something looks like it should work a certain way doesn't mean that's the case. Try telling that to your grandmother and her TV remote.
Example 6
A student was asked to remove all possible common factors from the following rational expression: The student wrote: . Identify the mistake, if any.
Answer
The student didn't pull out all the common factors. A factor of y can still be yanked from each term, to give . Why'd they overlook y? Tough to say, but it's probably some deep-rooted psychological issue. Maybe a y stole their lunch money.
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.
. The student wrote:
Identify the mistake, if any. 
The student wrote: 
Identify the mistake, if any.
The student wrote:
. Identify the mistake, if any.
. Why'd they overlook y? Tough to say, but it's probably some deep-rooted psychological issue. Maybe a y stole their lunch money.