Lesson: Simplifying Rational Expressions

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Hi Brent,

I like the approach of testing values! When can I use this approach in particular please.

Thank you for your advice
Best Regards
gmat-admin's picture

Great question!
Here's an article I wrote that specifically addresses that question: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values



[p + 5 + p³(−p − 5)]/(−p − 5) =

A. p + 5 + p³
B. P³ + 5
C. p³
D. p³ - 1
E. p³ - 5

Hi Brent, could you please explain what I am doing wrong in terms of my factoring approach to solve this question?

Step 1: p + 5 + p³(-p - 5)/(-p - 5)
Step 2: [(p + 5) + p³- 1(p + 5)]/(-1)(p + 5)
Step 3: [(p + 5)(1 + p³- 1)]/[(-1)(p + 5)] *In this step I factor out (p + 5) from the numerator
Step 4: (p + 5)(p³)/(-1)(p+5)

Here is where I get stuck.. appreciate your help.
gmat-admin's picture

Question link: https://gmatclub.com/forum/p-5-p-3-p-5-p-95022.html

NOTE: I added some brackets to your solution to reduce ambiguity.

You have a problem going from Step 1 to Step 2.
Notice that (-p - 5) = (-1)(p + 5)
So, Step 2 should look like this: [(p+5) + p³(-1)(p+5)]/(-1)(p+5)
We can simplify this to get: [(p+5) - p³(p+5)]/(-1)(p+5)
From here, we can factor the numerator to get: (p+5)[1 - p³]/(-1)(p+5)
Simplify: [1 - p³]/(-1)
Rewrite as: p³ - 1


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