**Canceling with Variables**

**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 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.

**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 Practice Problems**

**Practice**

**Solutions**

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

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