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Math Help - Partial Fractions- Please check my answers

  1. #1
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    Partial Fractions- Please check my answers

    Please check my answers.

    Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.

    (7x+5)/(x-2)(x+5)
    I got: (a)/(x-2) + (b)/(x+5)

    (4x-4)/(x^2+8x+12)
    I got: (a)/(x+6) + (b)/(x+2)

    Write the partial fraction decomposition of the rational expression.

    (x-6)/(x-2)(x-3)
    I got: (4)/(x-2) + (3)/(x-3)

    (x)/(x-5)(x-6)
    I got: (-5)/(x-5) + (6)/(x-6)

    (x)/(x^2-5x+6)
    I got: (-2)/(x-2) + (3)/(x-3)

    (11x-35)/(x-1)(x-4)
    I got: (8)/(x-1)+ (3)/(x-4)

    (12x+52)/(x^2+10x+24)
    I got: (2)/(x+4) + (10)/(x+6)

    Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.

    (6x-5)/(x+5)^2
    I got: (a)/(x+5) + (b)/(x+5)^2

    (4x+2)/(x+3)(x^2+x-3)
    I got: (a)/(x+3) + (b)/(x^2+x-3)
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by soly_sol View Post
    Write the partial fraction decomposition of the rational expression.


    (x-6)/(x-2)(x-3)
    I got: (4)/(x-2) + (3)/(x-3)
    the second must be -3

    Quote Originally Posted by soly_sol View Post
    Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.

    ....

    (4x+2)/(x+3)(x^2+x-3)
    I got: (a)/(x+3) + (b)/(x^2+x-3)
    it should be bx+c
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  3. #3
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    Hello, soly_sol!

    Write the form of the partial fraction decomposition of the rational expression.

    \frac{7x+5}{(x-2)(x+5)} . . . I got: . \frac{a}{x-2} + \frac{b}{x+5}

    \frac{4x-4}{x^2+8x+12} . . . I got: . \frac{a}{x+6} + \frac{b}{x+2} . . . . both correct!

    Write the partial fraction decomposition of the rational expression.

    \frac{x-6}{(x-2)(x-3)} . . . I got: . \frac{4}{x-2} {\color{red}\,+\,} \frac{3}{x-3}
    . . . . . . . . . . . . . . . . . . . .
    minus

    \frac{x}{(x-5)(x-6)} . . . I got: . \frac{-5}{x-5} + \frac{6}{x-6}

    \frac{x}{x^2-5x+6} . . . I got: . \frac{-2}{x-2} + \frac{3}{x-3}

    \frac{11x-35}{(x-1)(x-4)} . . . I got: . \frac{8}{x-1}+ \frac{3}{x-4}

    \frac{12x+52}{(x^2+10x+24} . . . I got: . \frac{2}{x+4} + \frac{10}{x+6} . . . . The rest are correct!

    Write the form of the partial fraction decomposition of the rational expression.
    It is not necessary to solve for the constants.

    \frac{6x-5}{(x+5)^2} . . . I got: . \frac{a}{x+5} + \frac{b}{(x+5)^2}

    \frac{4x+2}{(x+3)(x^2+x-3)} . . . I got: . \frac{a}{x+3} + \frac{b}{x^2+x-3} . . . . no

    For a quadratic denominator, we need two terms in the numerator.

    . . \frac{a}{x+3} + \frac{{\color{blue}bx + c}}{x^2+x-3}

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