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Which of the following must be equal to zero, where x is a non-zero in

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Which of the following must be equal to zero, where x is a non-zero in [#permalink] New post   10 Apr 2023, 23:50
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Which of the following must be equal to zero, where x is a non-zero integer?

Indicate all that apply

A. \(-\frac{1}{x}
\)

B. \(x+(-x)\)

C. \(\frac{2}{2x+1}-\frac{1}{x+0.5}\)

D. \(\frac{0}{x}\)
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B,C,D
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Re: Which of the following must be equal to zero, where x is a non-zero in [#permalink] New post   27 May 2023, 01:07
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Starting with D

0 divided by any number is still 0. So D is correct

C is 2/2(x+0.5)=1/(x+0.5). Therefore we subtract to equal quantities of opposite signs. C must be also 0

B essentially is x-x Therefore B must be = to 0 as well

A -1 divided by any number different from zero will be never zero itself

B, C, and D are the correct options
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Re: Which of the following must be equal to zero, where x is a non-zero in [#permalink] New post   20 Mar 2025, 09:51
Carcass didnt get how option c is equal to zero pls explain
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Re: Which of the following must be equal to zero, where x is a non-zero in [#permalink] New post   20 Mar 2025, 10:36
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C

\(\frac{2(x+0.5)-(2x+1)}{(2x+1)(x+0.5)}= \frac{2x+1-2x-1}{(2x+1)(x+0.5)}=\frac{0}{(2x+1)(x+0.5)}\)

The whole expression is = to zero

I hope this helps
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Re: Which of the following must be equal to zero, where x is a non-zero in [#permalink]
20 Mar 2025, 10:36
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