If \(\left(6+\frac{2}{x}\right)\left(x-4\right)=0,\) and

Gmat_mission wrote:If \(\left(6+\frac{2}{x}\right)\left(x-4\right)=0,\) and \(x\) does not equal \(4\), then \(x =\)

(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3

[spoiler]OA=C[/spoiler]

Source: Magoosh

We see that the product of two expressions is 0; for the product to be 0, at least one of the two expressions must be 0. Since x ≠ 0, the term x – 4 ≠ 0; thus, (6 + 2/x) must be 0.

(6 + 2/x) = 0 => x = –1/3

The correct answer: C

Hope this helps!

-Jay
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Gmat_mission wrote:If \(\left(6+\frac{2}{x}\right)\left(x-4\right)=0,\) and \(x\) does not equal \(4\), then \(x =\)

(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3

[spoiler]OA=C[/spoiler]

Source: Magoosh

Since x is not 4, then x - 4 is not zero and hence 6 + 2/x must be 0. Therefore, we have:

6 + 2/x = 0

2/x = -6

2 = -6x

x= 2/(-6) = -1/3

Answer: C