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For What value of X is fraction numerator 8 x plus 2 x squared over denominator left parenthesis x plus 4 right parenthesis open parentheses x squared minus 9 close parentheses end fraction undefined ?

  1. -8
  2. -3
  3. 0
  4. 4
  5. 9

hintHint:

The expansion of open parentheses x squared minus a squared close parentheses equals left parenthesis x minus a right parenthesis left parenthesis x plus a right parenthesis.
We are asked to find the value for which the expression is undefined.

The correct answer is: -3


    Step 1 of 2:
    Simplify the expression and cancel out the common factors,
    fraction numerator 8 x plus 2 x squared over denominator left parenthesis x plus 4 right parenthesis open parentheses x squared minus 9 close parentheses end fraction equals fraction numerator 2 x left parenthesis 4 plus x right parenthesis over denominator left parenthesis x plus 4 right parenthesis open parentheses x squared minus 3 squared close parentheses end fraction
    equals fraction numerator 2 x left parenthesis x plus 4 right parenthesis over denominator left parenthesis x plus 4 right parenthesis left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis end fraction

                                               equals fraction numerator 2 x over denominator left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis end fraction
    Thus, the simplified expression is fraction numerator 2 x over denominator left parenthesis x minus 3 right parenthesis left parenthesis x plus 3 right parenthesis end fraction.
    Step 2 of 2:
    The expression is undefined when the denominator is equal to zero. So, we have:
    (x - 3)(x + 3) = 0
                                                  x = -3 & x = 3
    Therefore, correct option is: b.

    Division of an expression by zero is not defined.

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