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About Steve Holleran
Expertise
I can help with all math questions from basic math to Calculus. Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.

Experience
33 years teaching experience in NJ public schools

Education/Credentials
B.S. Mathematics : Wake Forest University 1972 M.S. Mathematics : Monmouth University 1981

You are here: Experts > Science > Mathematics > Advanced Math > Partial fraction

Advanced Math - Partial fraction

Expert: Steve Holleran - 10/2/2008

Question
Express the following in partial fraction:

(x^2-x)/((x^2+3)(x^2+2))

i have tried it many times for hours, again & again still cant get it right. Much appreciated.

Answer
Hello,

I think it goes like this:

(x^2-x)/(x^2+3)(x^2+2) =(Ax + B)/(x^2 + 3)+(Cx + D)/(x^2+2)

          x^2 - x = (Ax + B)(x^2+2) + (Cx + D)(x^2 + 3)

     x^2 - x = Ax^3 + Bx^2 + 2Ax + 2B + Cx^3 + Dx^2 + 3Cx + 3D

     x^2 - x = x^3(A + C) + x^2(B + D) + x(2A + 3C) + (2B + 3D)

Then A + C = 0      B+ D = 1    2A - 3C = -1     2B + 3D = 0

Solving the A,C system:

     2A - 3C = -1   ------->   2A - 3C =-1

      A + C = 0    ----->    -2A -2C = 0
                             -------------

                                 -5C = -1 so C = 1/5 ,then A = -1/5

If you solve the B, D system, you get B = 3 and D = -2

So, the solution is

   (-1/5 x + 3)/(x^2 + 3)   + (1/5 x - 2)/(x^2 + 2)

Hope this helps
Steve

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