Ratio and Proportions:



Algebra 2 Name_______________________

13.1 Simplifying Rational Expressions Period 1 2 3 4 5 6 7

NOTES

Rational Expressions are like fractions, but the numerator and denominators will have monomials, binomials or trinomials in it. So the concept is like reducing a fraction, but involves a different process. Let’s start with 3 simple rules:

**A monomial can only cancel or reduce with another ______________.

**A binomial can only cancel with another ____________ that is exactly the same or it     remains as is.

**A trinomial can only cancel with another ____________ that is exactly the same or it     remains as is.

A Rational Expression is in Simplest Form when:

• All monomials are simplified within the expression

• All binomials and trinomials are completely factored and then common ones are cancelled

Steps to Simplify a Rational Expression:

1. Look at monomials and reduce the numbers, just like you do a regular fraction.

2. Look at the variables, if any, of any monomials and subtract exponents of common variables to simplify.

3. Look for any binomials that are exactly the same and cancel. These can be cancelled because anything divided by itself = 1.

4. Look for any trinomials that are exactly the same and cancel.

Examples:

Simplify each rational expression if possible. If it cannot be factored, write CBS.

a) [pic] b) [pic] c) [pic]

d) [pic] e) [pic]

f) [pic] g) [pic]

h) [pic] i) [pic]

j) [pic] k) [pic]

Algebra 2 Name_______________________

13.1 Reducing Rational Expressions Period 1 2 3 4 5 6 7

1. Explain why each of the following rational expressions cannot be further simplified.

a. [pic] b. [pic]

Explanation: Explanation:

2. Explain what part of the following rational expressions can be further simplified.

a. [pic] b. [pic]

Explanation: Explanation:

3. Circle the letter(s) of the rational expressions that can be further simplified. Then simplify. (More than 1 answer)

a. [pic] b. [pic] c. [pic]

4. Simplify the expression [pic].

a. [pic] b. [pic] c. [pic] d. [pic]

|Simplify the following expressions. If it cannot be simplified, write CBS. |

|**Remember, reduce or divide the numbers and subtract the exponents of the variables that are the same. |

|D Level |

|5. [pic] |6. [pic] |7. [pic] |8. [pic] |

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|9. [pic] |10. [pic] |11. [pic] |12. [pic] |

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|13. [pic] |14. [pic] |15. [pic] |

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|16. [pic] |17. [pic] |18. [pic] |

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|Mixed Review |

|19. Simplify. |20. Factor out the GCF. |21. Factor. |

| | |(GCF 1st / double bubble) |

|[pic] | | |

| |[pic] |[pic] |

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RANDOM ANSWERS (after first 4)

|a. Cannot cancel a binomial with a |4. a |CBS |[pic] |

|monomial | | | |

|  b. Cannot cancel a       trinomial | | | |

|with a       binomial and the | | | |

|      trinomial is not       factorable| | | |

| |[pic] |[pic] |[pic] |

|a. The binomials can cancel because |[pic] |[pic] |5(2x + 3) |

|they are exactly the same | | | |

|b. y3 and y can be      simplified by | | | |

|     subtracting the      exponents | | | |

| |[pic] |[pic] |[pic] |

|a. simplifies to |[pic] |[pic] | |

|[pic] | | | |

|    b. does not          simplify | | | |

|c. simplifies to | | | |

|[pic] | | | |

| |[pic] |3 | |

| |x |[pic] | |

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