Question

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

Answer 1

C.

Explanation:

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

`(2x+8)/(x^2-16)=(2(x+4))/((x-4)(x+4))=(2)/(x-4)\\\\(x^2+8x+16)/(x+4)=((x+4)^2)/(x+4)=x+4`

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

`(x^2-16)/(2x+8)\cdot(x+4)/(x^2+8x+16)=(x-4)/(2(x+4))`

This matches choice C.