Which of the following is equivalent to [1 – {1/ (x + 1)}]/x for all values of x for which both expressions are defined? (A) 1 (B) x + 1 (C) 1/x (D) 1/ (x + 1) (E) x^2 + x [spoiler]Source: https://readyforgmat.com[/spoiler]

[1 - {1/ (x + 1)}]/x =[x/x+1]/x =1/x+1 Pick D

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.