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Select the correct answer.
Consider this expression.
1 - 4
2(1 + 4)
For which product or quotient is this expression the simplest form?
A.
B.
25 + 8
2 + 81 + 16
12 – 16
.
I + 4
12 – 16 I + 4
.
21 + 8 r2 + 81 + 16
12 – 16 1 + 4
21 + 8 2 + 81 + 16
21 + 8 2 + 8 + 16
12 – 16
1 + 4
C.
.
OD

Select the correct answer Consider this expression 1 4 21 4 For which product or quotient is this expression the simplest form A B 25 8 2 81 16 12 16 I 4 12 16 class=

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sqdancefan

Answer:

  C.

Step-by-step explanation:

We can simplify each of the terms of choice A to see what relationship is required in order to obtain the desired result:

  [tex]\dfrac{2x+8}{x^2-16}=\dfrac{2(x+4)}{(x-4)(x+4)}=\dfrac{2}{x-4}\\\\\dfrac{x^2+8x+16}{x+4}=\dfrac{(x+4)^2}{x+4}=x+4[/tex]

The desired result, (x-4)/(2(x+4)) is the product of the reciprocals of these:

  [tex]\dfrac{x^2-16}{2x+8}\cdot\dfrac{x+4}{x^2+8x+16}=\dfrac{x-4}{2(x+4)}[/tex]

This matches choice C.

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