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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Reducing a Rational Expression to Lowest Terms

In each rational expression that follows, we will assume that no value of a variable will make a denominator 0.

Like a fraction in arithmetic, a rational expression is usually easier to work with when written in lowest terms.

The procedure for reducing a rational expression to lowest terms is like the procedure for reducing a fraction to lowest terms.

Procedure â€” To Reduce a Rational Expression to Lowest Terms

Step 1 Factor the numerator and denominator.

Step 2 Cancel all pairs of factors common to the numerator and denominator.

Note:

When we have reduced a rational expression to lowest terms, we also say we have simplified the rational expression.

Hereâ€™s an example from arithmetic.

Reduce to lowest terms:

 Step 1 Factor the numerator and denominator. Step 2 Cancel all pairs of factors common to the numerator and denominator.

Thus,

Remember, that w 0, x 0, and y 0.

We can also use the properties of exponents to simplify this fraction:

Example 1

Reduce to lowest terms:

Solution

 Step 1 Factor the numerator and denominator. Step 2 Cancel all pairs of factors common to the numerator and denominator.

Thus,

Example 2

Reduce to lowest terms:

Note:

Remember, it is understood that x 3 and x ≠ -3.

Solution

 Step 1 Factor the numerator and denominator. Step 2 Cancel all pairs of factors common to the numerator and denominator.

Thus,

Note:

Like a fraction in arithmetic, a rational expression should normally be written in lowest terms.