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Helga [31]
3 years ago
14

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

Mathematics
1 answer:
Nastasia [14]3 years ago
8 0

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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Tip: Do the following to visualize why this method works: Take an empty cereal box and push in the top flaps. If you then look into the empty box, the top of the box makes a rectangular shape, right? Now, start to crush the top of the box — you know, like you want to make it flat before putting it in the trash. As you start to crush the top of the box, you see a parallelogram shape. Now, after you’ve crushed it a bit, if you take this parallelogram and make one of the angles a right angle, the whole top has to become a rectangle again. You can’t make one of the angles a right angle without the other three also becoming right angles.

Step-by-step explanation:

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Same question
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<h2>Good evening ,</h2>

<em><u>Answer</u></em>:

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<em><u>Step-by-step explanation:</u></em>

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look at the photo for more details.

______________

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