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## Comment on

Simplifying Rational Expressions## 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

Fatima-Zahra

## Great question!

Great question!

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

Cheers,

Brent

## https://gmatclub.com/forum/p

[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.

## Question link: https:/

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

Cheers,

Brent

## https://gmatclub.com/forum/if

Hi Brent - really having a hard time understanding the factoring in the question in this link.

How does the numerator factor out that way? Not sure I see it.

Thanks

## Question link: https:/

Question link: https://gmatclub.com/forum/if-xy-0-what-is-the-value-of-x-4-y-2-xy-2-x-3...

Let's start with: x⁴y² - (xy)²

Rewrite as: x⁴y² - (xy)(xy)

Simplify: x⁴y² - x²y²

At this point, we can see that x²y² is the greatest common factor (GCF) of x⁴y² and x²y², which means we can factor it out.

Notice that x⁴y² = (x²y²)(x²)

And x²y² = (x²y²)(1)

So, we get: (x²y²)(x² - 1)

Here's the video on GCF factoring: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Does that help?

Cheers,

Brent

## Yes - I wasn't looking at it

One more additional question...why can't I factor out one of the x's in the numerator with the x from the denominator?

## We have: (x² - 1)/x

We have: (x² - 1)/x

We can't factor (in a nice way) the x out of x²-1

In order to do so, we must be able to write: x² - 1 = x(something)

We COULD so do like x² - 1 = x(x - 1/x), in which case we get:

(x² - 1)/x = x(x - 1/x)/x = x - 1/x

So, (x² - 1)/x and x - 1/x are equivalent expressions.

Does that help?

Cheers,

Brent

## Yes, this is helpful. Thank

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