SOLUTION: <pre>rationalize the denominator: 7 --------- &#8730;3 – &#8730;2</pre>

 
    7
---------
 √3 – √2


To rationalize a denominator with has two terms, you must

1. Form the conjugate surd
   A.  Write the denominator √3 - √2
   B. Change the sign of the second term only √3 + √2
   

2. Form the fraction by putting the conjugate surd over
   itself. 

    √3 + √2
   ---------   (Notice that this equals the number 1]
    √3 + √2

3. Multiply the original fraction by this fraction.  The
   value won't change because this amounts to multiplying
   by 1.

      7        √3 + √2
  --------- × ---------
   √3 – √2     √3 + √2

4. Indicate the multiplication of numerators ans denominators

       7(√3 + √2)
  -------------------
   (√3 – √2)(√3 + √2)    
  
5.  Multiply the top and the bottom  

           7√3 + 7√2
   ------------------------
      3 + √3√2 - √2√3 - 2

6. The middle two terms in the bottom cancel out

    7√3 + 7√2
   -----------
      3 - 2

    7√3 + 7√2
   -----------
        1

    7√3 + 7√2
  
Edwin
AnlytcPhil@aol.com