SOLUTION: <pre><b>Divide and Simplify: 5x - 7 ----------- 25x² - 49 ----------- ---- 5x² + 27x + 28</pre>

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Question 43227This question is from textbook INTERMEDIATE ALGEBRA
: 
Divide and Simplify: 

      5x - 7
   -----------
    25x² - 49
----------------
 5x² + 27x + 28
 This question is from textbook INTERMEDIATE ALGEBRA

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Divide and Simplify: 

      5x - 7
   -----------
    25x² - 49
----------------
 5x² + 27x + 28

Write it as the upper fraction divided
by the the trinomial at the bottom:


      5x - 7       
   ----------- ÷ (5x² + 27x + 28)
    25x² - 49             

Now put that trinomial over 1:

      5x - 7      5x² + 27x + 28
   ----------- ÷ ----------------
    25x² - 49            1

Now invert the second fraction and 
change the ÷ to ×

      5x - 7             1
   ----------- × ----------------
    25x² - 49     5x² + 27x + 28       

Factor the two denominators

          5x - 7                1
   ------------------ × -----------------
    (5x - 7)(5x + 7)     (x + 4)(5x + 7)

Write as one fraction by indicating the 
multiplicatiom of numerators and
denominators:

                 5x - 7                
   ---------------------------------
    (5x - 7)(5x + 7)(x + 4)(5x + 7)

Cancel the (5x - 7)'s
 
                    1
                 5x - 7                
   ---------------------------------
    (5x - 7)(5x + 7)(x + 4)(5x + 7) 
        1

                  1                
       -------------------------
        (5x + 7)(x + 4)(5x + 7)

Since there are two factors (5x + 7) you
can write their product as (5x + 7)²

                  1                
          ------------------
           (x + 4)(5x + 7)²

Edwin
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