9-4       

           ADDING AND SUBTRACTING RATIONAL EXPRESSIONS

                                                                 Squint Quint N. 

 ex.1.    1/A + 1/B = 1/C  
                            1/A = 1/C - 1/B        subtract 1/B from both sides. 
                            1/A = 1/10 - 1/20     C = 10  and B = 20. we just picked random numbers to plug in.
                                    = 1 * 4/ 10 * 4   -  1 * 2/ 20 * 2  Find the number that goes into both number and then dived them. For this problem it would be 5. so we divided 10 and 20 by 5 and got 2 and 4.      
                        then     = 4/40 - 2/40  we solved it out. 
                     so then    = 2/40   this is the final answer. 4-2 is 2 and 40 was the common denominator.                                     

                      Read and GRASP the problem                  

 ex.2.  --- When Squint and Phil hill work together they painted  fence in 8 hours. Last year, Phil hill painted the fence alone. The year before that Squint painted it alone, but took 12 hours less than  Phil hill took. How long did Squint and Phil hill take, when they painted alone. 

             Squint can paint it in "s" hours, so he does 1/s per hour. Phil hill paints it in "p" hours, so he does 1/p per hour. Then, working together, they do 1/s + 1/p = 1/8 per hour, since they took 8 hours. We also know that Phil hill takes 12 hours longer then Squint, so p = s + 12. Then we get 1/s + 1/(s +12) = 1/8. 

                 hours to complete job:
                         Squint: s
                        Phil hill: s + 12
                       together: 8

                completed per hour:
                         Squint: 1/s
                         Phil hill: 1/(s + 12)
                       together: 1/8 

              adding their labor:        
                     1/s + 1(s +12) = 1/8

To solve for "s" , We multiply through by 8s(s + 12) to get rid of all of the denominators:
                                8(s + 12) + 8(s) = (s)(s +12)

                               8s +96 +8s = s² + 12s

                               16s + 96 = s² + 12s 

                               0 = s² - 4s - 96

                              (s-12)(s + 8) = 0     factoring. 

Then s = 12 and a = -8.  In this problem, "s" must be positive, so we don't need the "s + -8 solution.

                          Squint takes 12 hours, and Phil hill takes 24 hours.

                                                                " Shoot for the moon.
                                                Even if you miss, you'll land among the stars."
                                                                      Les Brown

                           INSPIRATIONAL QUOTE - this quote represents courage and how you should never give up on your goals even if you don't completely succeed. 

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