GMAT OFFICIAL GUIDE PS

Solution:

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

Answer: C

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

About The Author

Jeffrey Miller is the head GMAT instructor for Target Test Prep. Jeff has more than fourteen years of experience in the business of helping students with low GMAT scores hurdle the seemingly impossible and achieve the scores they need to get into the top 20 business school programs in the world, including HBS, Stanford, Wharton, and Columbia. Jeff has cultivated many successful business school graduates through his GMAT instruction, and will be a pivotal resource for many more to follow.