The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 6.5: SIMPLIFYING ALGEBRAIC FRACTIONS -------------------------------------------------------------------------------------

You can simplify algebraic fractions by factoring and cancelling the common factors. Assume that the denominator of the fraction is not equal to 0.

EXAMPLES 8 + 4 x 4(2+x) 6(x+ 2)

== =

6 x+ 12

2 · 2(2 +x) 2 · 3(x + 2)

2

3

x^2 + 11 x+ 24 (x+ 8) (x+ 3) (x+ 2) (x+ 3) (x+ 2)

==(x+ 8) x^2 + 5 x+ 6

DIRECTIONS: Simplify each fraction.

2 x− 8 12 x− 4 2.

4 x+ 1 8 x+ 2

3. 5 x− 5 y 6 x− 6 y

4. 2 x^3 +x^2 6 x^3 + 4 x^2

5. x^2 −y^2 x−y

6. x^2 +x− 6 x^2 + 2 x− 8

7. 3 x^2 + 5 x− 12 3 + 4 x+x^2 8. x^2 − 10 x+ 25 x− 5

CHALLENGE:Do you agree that

2 x^2 − 10 x+ 8 x^2 + 4 x− 5

is expressed in simplest form

as

2(x^2 − 5 x+4) x^2 + 4 x− 5

?Explainyouranswer.

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