Math Analysis

Find two rational expressions that have a sum of 9-9x/x^2-9

I need steps not just answers

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asked by Mary
  1. First, I assume you mean (9-9x)/(x^2-9)?

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    posted by Ryan
  2. Making the same assumption as Ryan
    9[(1-x)]/(x-3)(x+3)=9[a/(x-3)+b/(x+3)]
    a(x+3) + b(x-3) = 1-x
    a+b=-1
    3a-3b=1
    solve and get a =-1/3, b=-2/3
    so
    9 [(-1/3)/(x-3) -(2/3)/(x+3)]
    = -3/(x-3) -6/(x+3)

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    posted by Damon
  3. If my assumption is true, you could simply use 9/(x^2-9) + -9x/(x^2+9), as these are both rational expressions, I think.

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    posted by Ryan

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