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Math Help - Partial Fraction Decompostion

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    Partial Fraction Decompostion

    I need help with these...

    Partial Fraction Decomposition:

    1/4x^2-9

    and

    -2x+15/x^2-x-12
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  2. #2
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    Quote Originally Posted by RenSully View Post
    I need help with these...

    Partial Fraction Decomposition:

    1/4x^2-9

    and

    -2x+15/x^2-x-12
    Hi RenSully,

    Here's the second one:

    If all the factors are of the form ( x - c ), then each of the partial fractions will be of the form \frac{A}{x-c}.


    \frac{-2x+15}{x^2-x-12}=\frac{-2x+15}{(x-4)(x+3)}\Rightarrow\frac{A}{x-4}+\frac{B}{x+3}

    First, multiply the original proper fraction by ( x - c ) and evaluate the result at x = c to get the value of the constant.

    \frac{-2x+15}{(x-4)(x+3)}(x-4)=\frac{-2x+15}{x+3}\Rightarrow A=\frac{-2(4)+15}{4+3}=1

    \frac{-2x+15}{(x-4)(x+3)}(x+3)=\frac{-2x+15}{x-4}\Rightarrow B=\frac{-2(-3)+15}{-3-4}=-3

    Thus:

    \frac{-2x+15}{x^2-x-12}=\frac{1}{x-4}+\frac{-3}{x+3}
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