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Inequalities & Absolute Value

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Rational Expressions 1

Rat'l. Exp. 2 - mult&div

Rat'l. Exp. 3 - add&subt

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 UNIT 1  : PRECALCULUS PREP

 LESSON 7: RATIONAL EXPRESSIONS 3 HOMEWORK QUESTIONS

 

Text Box: Adding and Subtracting Rational Expressions with LIKE DENOMINATORS: · Keep the common denominator · Add or subtract the numerators · State any restrictions – remember the denominators cannot equal 0.
 

 

 

 

 

 

 

 

 

Text Box: Adding and Subtracting Rational Expressions with UNLIKE DENOMINATORS: · Factor each denominator · LCD ---ΰTake the highest exponent of each factor for algebraic factors · LCD ---ΰFor numerical factors, take the LCD of the numbers · Add or subtract the numerators, simplifying fully · State any restrictions – remember the denominators cannot equal 0.
 

 

 

 

 

 

 

 

 

 


Homework Questions:

 

1.  Simplify and state the restrictions:

                                                                 

 

2.  Simplify and state the restrictions:

                                         

 

3.  Simplify and state the restrictions:

                                    

 

4.  Simplify and state the restrictions:

                              

 

 

6.  Simplify and state the restrictions:

                                   

 

 

Solutions:

 

1.  Simplify and state the restrictions:

 

                                                                 

 

Solutions:

Text Box: ** LCD of 4 and 3 is 12; also include highest exponent of a ΰ a3. LCD = 12a3                               

      

Text Box: LCD = 8(m+1)(m-3) Numerical LCD is 8; LCD for (m+1) and (m-3) is (m+1)(m-3)      

 

 

 

Text Box: LCD = (x-4)(x+3)(x-2)       

 

2.  Simplify and state the restrictions:

                                         

Solutions:

Text Box: LCD of 5 and 3 is 15; the highest power of x is x3. Therefore the LCD = 15x3      

 

Text Box: LCD of 2 and 6 is 6 The highest power of a is a2 The highest power of b is b3 Therefore LCD = 6a2b3                                               

 

Text Box: · Fully factor denominators · Numerical LCD is 4 · The highest exponent of (x+4) is (x+4)2                    

 

3.  Simplify and state the restrictions:

                                    

Solutions:         

Text Box: LCD = 2(a-3)(a+3)                       

 

 

Text Box: LCD = (x-5)(x-2)(x+5)                      

 

 

 

 

 

4.  Simplify and state the restrictions:

                              

 

Solutions:         

 

Text Box: 4x2 - 8x - 5 = 4x2 –10x + 2x –5 = 2x(2x – 5) + 1(2x-5) = (2x – 5)(2x + 1)           

 

Text Box: 6x2 + 13x – 5 = 6x2 +15x – 2x –5 = 3x(2x + 5) – 1(2x + 5) = (2x + 5)(3x – 1) 6x2 + 7x – 3 = 6x2 + 9x – 2x – 3 = 3x(2x + 3) – 1(2x + 3) = (2x + 3)(3x – 1)                

 

 

 

Solution:         

 

 

6.  Simplify and state the restrictions:

                                   

 

Solutions:         

 

 

 

 

 

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