Question: Simplify a Rational Expression

Comment on Simplify a Rational Expression

Dear Brent,

Another approach is to substitute X with 1. Then you get 5/9 as your target, and only answer D results in 5/9. What do you think of this strategy in general? Do you prefer the algebraic approach to substituting X with an easy number, such as 1? Are there any drawbacks of this approach.

Although, I could fully simplify this particular equation I have also come across some equations that I started simplifying algebraically, but somewhere along the way made a mistake, and therefore lost a lot of time and used up a lot of space on my scratch paper. Hence, I wonder what I should do on test day.

gmat-admin's picture

Your strategy is perfect. The only drawback is that it's possible that plugging x = 1 would have resulted in more than one answer choice yielding the right output of 5/9, in which case, you would have to plug in a second (and perhaps even a third value) to determine the correct answer. All of this could be quite time consuming.

That said, your strategy can often yield the correct answer quickly. So, be sure to keep it in your mathematical toolbox.

Thank you for your swift reply and helpful feedback!

I get really confused sometimes with factorizing large numbers so i use values such as 1 or 2 to get to the answer is this a right option instead of factoring out?
gmat-admin's picture

That strategy will work. The main problem with that approach is that even plugging a small number (e.g., 2) into an expression can get pretty crazy if the exponents are sufficiently large.

Also, to answer other questions, it will be very useful to have mastered all of the factoring techniques covered in videos #7 to #10 in the algebra module (https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving)

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