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Math Help - Polynomials

  1. #1
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    Polynomials

    For the following rational expressions, perform the indicated operation and simplify the result:

    a) ył-1 y-1
    __________ ______
    y˛ + y - 6 divided by 3+y




    b) are there any restrictions on the variable y?


    Hey guys i need help on how to do this, i have no idea where to start
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  2. #2
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    Quote Originally Posted by Cockchestner007 View Post
    For the following rational expressions, perform the indicated operation and simplify the result:

    a) ył-1 y-1
    __________ ______
    y˛ + y - 6 divided by 3+y




    b) are there any restrictions on the variable y?


    Hey guys i need help on how to do this, i have no idea where to start
    its y-1 / 3+y
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Cockchestner007 View Post
    For the following rational expressions, perform the indicated operation and simplify the result:

    a) ył-1 y-1
    __________ ______
    y˛ + y - 6 divided by 3+y


    b) are there any restrictions on the variable y?

    Hey guys i need help on how to do this, i have no idea where to start
    Hi Cockchestner007,

    I'm having a wee bit of trouble untangling what you have.
    Is it this?

    \frac{y^3-1}{y^2+y-6} \div \frac{y-1}{3+y}

    If not, you might want to use grouping symbols to show exactly what you have.
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  4. #4
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    yes!! thats exactly what i have
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  5. #5
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    Hi Cockchestner007,


    \frac{y^3-1}{y^2+y-6} \div \frac{y-1}{3+y}

    Invert the divisor and multiply.

    \frac{y^3-1}{y^2+y-6} \cdot \frac{y+3}{y-1}

    \frac{(y-1)(y^2+y+1)}{(y+3)(y-2)} \cdot \frac{y+3}{y-1}

    The "restrictions of the variable" means "what would y have to be to make the denominator of either fraction zero?"

    Those restrictions would be: y cannot be -3, 2, or 1
    Simplifying we arrive at:

    \frac{y^2+y+1}{y-2}

    The only restriction after simplification is y cannot be 2.
    If we were talking about rational functions, this would be a vertical asymptote.

    The other two restrictions would be points of discontinuity on the graph.

    But, this may be too much information since these are only expressions.
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