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Math Help - Rational Expression

  1. #1
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    Rational Expression

    Determine whether the given expressions are proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression.

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

    (2) 2x(x^2 + 4)/(x^2 + 1)
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  2. #2
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    Quote Originally Posted by magentarita View Post
    Determine whether the given expressions are proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression.

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

    (2) 2x(x^2 + 4)/(x^2 + 1)
    Improper Rational Expression
    A rational expression in which the degree of the numerator polynomial is greater than or equal to the degree of the denominator polynomial.

    Note: Polynomial long division can be used to write an improper rational expression as the sum of a polynomial and a proper rational expression. Synthetic division may also be used for some fractions.

    Proper Rational Expression
    A rational expression in which the degree of the numerator polynomial is less than the degree of the denominator polynomial.

    (1) Proper Rational Expression

    (2) Improper Rational Expression

    \frac{2x(x^2+4)}{x^2+1}=\frac{2x^3+8x}{x^2+1}

    Now, perform long division to arrive at:

    2x+\frac{6x}{x^2+1}
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  3. #3
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    ok now....

    Quote Originally Posted by masters View Post
    Improper Rational Expression

    A rational expression in which the degree of the numerator polynomial is greater than or equal to the degree of the denominator polynomial.

    Note: Polynomial long division can be used to write an improper rational expression as the sum of a polynomial and a proper rational expression. Synthetic division may also be used for some fractions.

    Proper Rational Expression
    A rational expression in which the degree of the numerator polynomial is less than the degree of the denominator polynomial.

    (1) Proper Rational Expression

    (2) Improper Rational Expression

    \frac{2x(x^2+4)}{x^2+1}=\frac{2x^3+8x}{x^2+1}

    Now, perform long division to arrive at:

    2x+\frac{6x}{x^2+1}
    This is the exact detail that I look forward to each time I post questions.

    My precalculus course is coming to an end in a few weeks.
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  4. #4
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    Quote Originally Posted by magentarita View Post
    This is the exact detail that I look forward to each time I post questions.

    My precalculus course is coming to an end in a few weeks.
    Thanks a bunch. I didn't post the details of the polynomial long division. I sort of assumed you could do that.
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