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Math Help - Is this correct? (Partial fractions).

  1. #1
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    Is this correct? (Partial fractions).

    I was asked to resolve \frac{2x+1}{(2x+6)(x^2+4)} into partial fractions. I got: \frac{2x+1}{(2x+6)(x^2+4)} \equiv \frac{-11}{(13)(2x+6)}+\frac{11x+19}{(26)(x^2+4)}. Is it right?
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  2. #2
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    Actually it's not correct. If you fill in some number for x, you can verify that those equations are not the same.
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  3. #3
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    No.
    You can check by assigning a value to x; use x = 1 (easier)
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  4. #4
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    A correct approach would be:
    \frac{2x+1}{(2x+6)(x^{2}+4)} = \frac{2x+1}{(2x+6)} \cdot \frac{1}{x^{2}+4}
    \frac{2x+1}{(2x+6)} \cdot \frac{1}{x^{2}+4} = \frac{1}{2} \cdot \frac{2x+1}{x+3} \cdot \frac{1}{x^{2}+4}

    here is a start, I haven't tried to solve it further.
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  5. #5
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    Ah, little silly mistake.
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  6. #6
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    Thought

    I believe you're missing a term on the far R.H.S.
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  7. #7
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    Quote Originally Posted by wonderboy1953 View Post
    I believe you're missing a term on the far R.H.S.
    I wrote the wrong thing down. It was \frac{4x+1}{(2x+6)(x^2+4)} and I got \frac{4x+1}{(2x+6)(x^2+4)} \equiv \frac{-11}{13(2x+6)}+\frac{33x+57}{78(x^2+4)}
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