A reasonable expression is a portion where the numerator and also thedenominator space polynomials. To reduce a reasonable expression come lowestterms is comparable to reduce an arithmetic fraction to shortest terms.

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Procedure

To reduce a reasonable Expression to Lowest terms

Step 1 Factor the numerator and also denominator.

Step 2 Cancel pairs of determinants that are common to the numeratorand denominator.

Example 1

Reduce to shortest terms:


Solution
Step 1 aspect the numerator and also denominator.
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Step 2 Cancel common factors.
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Simplify.
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Thus, the an outcome is
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Note:

To element x2 - 2x - 15:

• uncover two integers who product is -15 and also whose amount is -2.They space 3 and -5.

• use these integers to create thefactorization (x + 3)(x - 5). To aspect x2 - 7x + 10:

• find two integers whose product is 10and whose sum is -7.They are -2 and also -5.

• usage these integers to write thefactorization (x - 2)(x - 5).

Example 2

Reduce to lowest terms:


Solution
Step 1 aspect the numerator and denominator.
Factor -1 out of the numerator.

Notice the in the numerator, -8 + x,can be written as x - 8.

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Step 2 Cancel usual factors.
Cancel the typical factor that x - 8. Simplify.
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= -1

So, the portion reduces come -1. Note:

Notice the in , the numerator anddenominator space opposites.Therefore, reduces come -1.

Example 3

Reduce to lowest terms:
Solution
Step 1 Factor the numerator and also denominator.

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Factor.

In the numerator, create 4 - xas -1(x - 4).

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Step 2 Cancel typical factors.
Cancel the usual factor the x 4. Simplify.
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Thus, the portion reduces to
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.Notice that 4 - x can be composed as aproduct wherein one variable is x - 4: 4 - x = -1(-4 + x) = -1(x - 4)