Math 142
Partial Fractions Examples

  1. Integrate using partial fractions

                           

    We have, for some A and B.

    So,

    Now letting x=3, we get A=2; and letting x=4, we get B=5.

    So, .


    Hence,

    Note that we can simpliy this last expression to .


      Two hydrogen atoms were walking along the street one day, and suddenly the one
      of the right says: Ohmigosh! I lost an electron!
      The one on the left says.. "Are you sure??"
      The one on the right replies: "Yes, yes! I'm positive!"

  • Suppose we want to express as a sum of partial fractions.





    Now letting x=2 on both sides, we see that 15 = 5D, and so D = 3.

    Now expanding the Right-Hand-Side we get



    So,                        

    Substituting D=3 into these gives,

                                 

    Solving these three equations simultaneously gives A=2, B=3, C=2 (and previously D=3)

    So, , and we have


         


  • Express a sum of partial fractions - but do not solve for the constants.


    Answer:

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                perfect practice makes perfect.
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                If the only tool you have is a hammer,
                you tend to see every problem as a nail.
                      ABRAHAM MASLOW
  • Express as a sum of partial fractions (you must solve for the constants).



    Let x=2 on both sides and we get, , so .

    Also, expanding the product on the right,

    Now compare the coefficients on both sides of this identity.

    So,

    And,

    So,



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