f(x)=2x^2+4x-16 g(x)=4x^2-16 Find (f/g)(x).

Question

f(x)=2x^2+4x-16
g(x)=4x^2-16
Find (f/g)(x).

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Yến Oanh 3 years 2021-08-25T08:53:24+00:00 1 Answers 6 views 0

Answers ( )

  1. trungdung22
    0
    2021-08-25T08:54:25+00:00
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    Answer:

    Step-by-step explanation:

    (\frac{f}{g} )(x) = \frac{2x^{2} +4x-16}{4x^{2} -16}

    2x²+4x -16 =  2(x²+2x-8); factor 2

                      = 2(x+4)(x-2) ;factor the quadratic equation

    4x²-16  = 4(x²-4) ; factor 4

                =4(x²- 2²) ; rewrite 4 as 2²

               = 4(x-2)(x+2); now use the difference of two squares a²-b²=(a-b)(a+b)

    so now we have:

    (\frac{f}{g}) (x) = \frac{2(x+4)(x-2)}{4(x-2)(x+2)} ; simplify (x-2) from numerator and denominator

                                      and 2/4 as 1/2

    (\frac{f}{g}) (x) = \frac{(x+4)}{2(x+2)}

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )