Hey guys,
Nice work on choice D! A few strategic thoughts on this one:
1) They don't give you an equation, but rather an expression and ask you what it equals. This means that your job isn't to solve for a variable, but rather to simplify the expression. Simplicity is your goal - and when you're using algebra you should always have a goal in mind so that the steps you take have a direction.
2) One easy way to simplify an expression like this is to reduce the number of terms. Here you have two terms in the numerator (1 and 1/(x+1) and one in the denominator. To simplify the numerator, you can find a common denominator for the two subtracted terms:
1 - 1/(x+1)
(x+1) / (x+1) - 1/(x+1) ---> Use x+1 as your common denominator
x / (x+1) ----> subtract the two terms
Now you have:
[x/(x+1)] / x
At this point, all of your terms are multiplication/division, so you can simplify by taking the denominator and multiplying it as a reciprocal:
x/(x+1) * 1/x
The x term in the numerator of the first and the denominator of the second will cancel, leaving:
1/(x+1)
Which is answer choice D.
The keys here are to:
1) Recognize that it's not an equation, but rather an expression that needs to be simplified
2) Take steps to simplify by:
-Reducing the number of terms
-Eliminating denominators
Quite often this test will rely on your ability to use algebra for a goal - either to solve for a variable or simplify an expression. When you see that in play, have a goal in mind and take algebraic steps to get there.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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