Canceling with Variables Help
Canceling with Variables
Variables can be canceled in fractions just as whole numbers can be.
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 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.
The reason 2 + 3 x can be canceled is that 2 + 3 x is a factor of (2 + 3 x )( x – 1).
Canceling with Variables Practice Problems
Practice problems for this concept can be found at: Algebra Introduction to Variables Practice Test.
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