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TSI Pre-Assessment Activity

Math Review

Rational Expressions

Section 1: Simplifiying Rational Expressions

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Write Rational Expressions in Lowest Terms

Just like arithmetic fractions, rational expressions should be written in lowest terms. The following property explains why we are able to simplify rational expressions.

Fundamental Property of Rational Numbers

If a/b is a rational number and if c is any nonzero real number, then

a/b = (ac)/(bc) =(a divided by c)/(b divided by c) = a/b

 

That is, the numerator and denominator of a rational number may either be multiplied or divided by the same nonzero number without changing the value of the rational number.

The following steps will help you to write rational expressions in lowest terms:

Write a Rational Expression in Lowest Terms

Step 1

Factor both the numerator and denominator to find their greatest common factor (GCF).

Step 2 Apply the fundamental property of rational numbers.

 


Example 1:

Write the rational expression in lowest terms:

8k/16

Solution:

The GCF of both the numerator and denominator is 8. Therefore, we can use the fundamental property of rational numbers to divide both the numerator and denominator by 8, thus cancelling out the GCF.

8k/16 with common factors cancelled= k/2


Example 2 :

Write the rational expression in lowest terms:

(a^2-a-6)/(a^2+5a+6)

 

Solution:

We can rewrite both the numerator and denominator by factoring to see what the GCF is and then simplify by using the fundamental property of rational numbers to cancel the GCF.

(a^2-a-6)/(a^2+5a+6)

= [(a-3)(a+2)]/[(a+3)(a+2)] with common factors cancelled

= (a-3)/(a+3)


Example 3 :

Write the rational expression in lowest terms: (m-3)/(3-m)

Solution:

We can rewrite both the numerator and denominator by factoring to see what the GCF is and then simplify by using the fundamental property of rational numbers to cancel the GCF.

(m-3)/(3-m)

= (m-3)/[-1(m-3)]      Factor out –1 from the denominator.

= (m-3)/[-1(m-3)] with common factors cancelled      Cancel out the GCF .

= 1 divided by -1      

= – 1


 

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