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If 1/x - 1/(x+1) (OG16)

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by [email protected] » Thu May 19, 2016 5:05 pm
Hi boomgoesthegmat,

I'm going to give you some hints so that you can try this question on your own:

[spoiler] The GMAT does NOT test you on the concept of 'undefined' numbers, so you won't have to deal with a calculation that is divided by 0. In this prompt, you'll notice that there are 3 fractions, but since none of them can be "over 0", we can eliminate the answers that would cause that to happen: 0, -1 and -4.

That means there are only two possibilities: -2 or -3. By plugging those values into the equation, you should quickly be able to determine which one 'balances' out the equation. THAT answer will be your solution....

Final Answer: C
[/spoiler]

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by OptimusPrep » Thu May 19, 2016 8:02 pm
boomgoesthegmat wrote:If 1/x - 1/(x+1) = 1/(x+4), then x could be

A) 0
B) -1
C) -2
D) -3
E) -4

OA: C
1/x - 1/(x+1) = 1/(x+4)
You can do this question both by testing values and algebraically.
I will solve it algebraically

x + 1 - x / (x)(x + 1) = 1/(x + 4)
1/x*(x + 1) = 1/(x + 4)

x + 4 = x^2 + x
x^2 = 4

x = 2 or -2

Correct Option: C
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If 1/x - 1/(x+1) (OG16)

by Brent@GMATPrepNow » Wed Aug 23, 2017 5:05 pm
boomgoesthegmat wrote:If 1/x - 1/(x+1) = 1/(x+4), then x could be

A) 0
B) -1
C) -2
D) -3
E) -4

OA: C
Plugging in the answer choices is definitely faster, but here's an algebraic solution...

One way to eliminate fractions is to multiply both sides by the least common multiple (LCM) of all the denominators.
The LCM of x, x+1 and x+4 is (x)(x+1)(x+4)

Given: 1/x - 1/(x+1) = 1/(x+4)
Multiply both sides by (x)(x+1)(x+4) to get: (x)(x+1)(x+4)[1/x - 1/(x+1)] = (x)(x+1)(x+4)[1/(x+4)]
Simplify: (x+1)(x+4) - (x)(x+4) = (x)(x+1)
Expand: [x² + 5x + 4] - [x² + 4x] = x² + x
Simplify: x + 4 = x² + x
Rearrange: x² = 4
Solve: x = 2 OR x = -2

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Tue Jul 17, 2018 3:42 pm
boomgoesthegmat wrote:If 1/x - 1/(x+1) = 1/(x+4), then x could be

A) 0
B) -1
C) -2
D) -3
E) -4
We must first eliminate the fractions in the equation 1/x - 1/(x+1) = 1/(x+4).

Thus, we will multiply the entire equation by the least common multiple of the denominators, which is:

x(x+1)(x+4)

We are now left with:

(x+1)(x+4) - x(x+4) = x(x+1)

x^2 + 5x + 4 - x^2 - 4x = x^2 + x

x + 4 = x^2 + x

4 = x^2

√4 = √x^2

x = 2 or x = -2

Alternate Solution:

Another option is to backsolve, substituting the answer choices into the given equation:

First, we can eliminate choices A, B and E because any one of them will make one of the denominators equal to 0 and we can't have denominator = 0. Choice A will make the denominator of the first fraction on the left hand side of the equation equal to 0; choice B will make the denominator of the second fraction on the left hand side of the equation equal to 0; and choice E will make the denominator of the fraction on the right hand side of the equation equal to 0.

So we only need to test choices C and D.

C. -2

1/(-2) - 1/(-2+1) = 1/(-2+4) ?

-1/2 - 1/(-1) = 1/2 ?

-1/2 + 1 = 1/2 ?

1/2 = 1/2 (Yes!)

We see that C is the correct choice, but let's show that D will not be the correct choice.

D. -3

1/(-3) - 1/(-3+1) = 1/(-3+4) ?

-1/3 - 1/(-2) = 1/1 ?

-1/3 + 1/2 = 1 ?

1/6 = 1 (No!)

Answer: C

Jeffrey Miller
Head of GMAT Instruction
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