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Canceling with Variables Help

By — McGraw-Hill Professional
Updated on Sep 26, 2011

Canceling with Variables

Variables can be canceled in fractions just as whole numbers can be.

Examples

Canceling with Variables Examples

When you see a plus or minus sign in a fraction, be very careful when you cancel. For example in the expression Canceling with Variables Examples , x cannot be canceled. The only quantities that can be canceled are factors. Many students mistakenly “cancel” the x and conclude that Canceling with Variables Examples or Canceling with Variables Examples . These equations are false. If Canceling with Variables Examples 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: Canceling with Variables Examples .

We can see that Canceling with Variables Examples and Canceling with Variables Examples . 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 Canceling with Variables Examples , you must rewrite the fraction:

Canceling with Variables Examples

Simply because a plus or minus sign appears in a fraction does not automatically mean that canceling is not appropriate. For instance Canceling with Variables Examples because any nonzero quantity divided by itself is one.

Examples

Canceling with Variables Examples

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 Examples

Canceling with Variables Practice Problems

Practice

Canceling with Variables Practice

Solutions

Canceling with Variables Solutions

Practice problems for this concept can be found at: Algebra Introduction to Variables Practice Test.

 

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