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Question

Explain how you can use your graphing calculator to show that the rational  expressions fraction numerator negative 6 x squared plus 21 x over denominator 3 x end fraction and
negative 2 x plus 7are equivalent under a given domain. What is true about the graph
at x = 0and Why?

hintHint:

Multiplying top and bottom of the expression by the same number or value will result in equivalent expression.
We are asked to explain why the given expressions are equivalent, what is true about the graph at x = 0  and explain.

The correct answer is: The graph at x = 0, will have a value y =7.


    Step 1 of 2:
    Simplify the expression fraction numerator negative 6 x squared plus 21 x over denominator 3 x end fraction
    fraction numerator negative 6 x squared plus 21 x over denominator 3 x end fraction equals fraction numerator 3 x left parenthesis negative 2 x plus 7 right parenthesis over denominator 3 x end fraction
    equals negative 2 x plus 7
    Once we simplified it, we got it reduced asequals negative 2 x plus 7.
    Hence, they are equivalent.
    Step 2 of 2:
    The domains of both the expressions are set of real numbers.
    Considering the expression equals negative 2 x plus 7, it is clear that it’s a polynomial. Hence, the domain would be set of real numbers.
    For the expressionfraction numerator negative 6 x squared plus 21 x over denominator 3 x end fraction, we could simplify the expression to negative 2 straight x plus 7 which again is a polynomial.
    The graph at  x = 0, will have a value y=7.

    The domain of any polynomial is set of real numbers.

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