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Set the denominator equal to zero.

Mathematics

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Answer

C

Step-by-step solution

3 steps

To find when the expression 5x+36x(x+1)\frac{5x+3}{6x(x+1)} will be undefined, we need to determine the values of xx that make the denominator equal to zero.

  1. Set the denominator equal to zero.

    6x(x+1)=06x(x+1) = 0

  2. Solve for xx.

    For the product of terms to be zero, at least one of the terms must be zero.
    So, either 6x=06x = 0 or x+1=0x+1 = 0.

  3. Solve each equation for xx.

    For the first case:

    6x=06x = 0 x=06x = \frac{0}{6} x=0x = 0

    For the second case:

    x+1=0x+1 = 0 x=−1x = -1

    Therefore, the expression is undefined when x=0x = 0 or x=−1x = -1.
    The set of values for xx is {0,−1}\{0, -1\}.

    Comparing this with the given options:
    A. {−3,0}\{-3, 0\}
    B. {−3,−1}\{-3, -1\}
    C. {0,−1}\{0, -1\}
    D. {0,1}\{0, 1\}

    The correct option is C.

    The final answer is C. {0,−1}\boxed{\text{C. } \{0, -1\}}.

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