Lesson: Simplifying Rational Expressions

Comment on Simplifying Rational Expressions

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If we plug in numbers to an equation & end up with the below results, is it correct to conclude that the answer is D without having to test additional numbers?

Quantity A: 3/2
Quantity B: 3/0
greenlight-admin's picture

Excellent question.

I'm reluctant to provide a blanket response, since it's possible that I haven't considered every possibility.

That said, most of the time (perhaps even ALL of the time), when there's a variable in the denominator, the test-makers will include some kind of proviso that ensures that the denominator does not equal zero.

Rather than try to build an absolute rule around your idea, I think it's better to plug in more than 1 set of values.

ASIDE: If you had a question that looked like this...

QUANTITY A: 3/x
QUANTITY B: 3/y

...it's very likely that there would be a proviso that says something like x ≠ 0 and y ≠ 0 (or the more concise version: xy ≠ 0), However, even if there were no such proviso, we can quickly plug in two sets of values to show that the correct answer is D..

Cheers,
Brent

Hi, I have a question regarding ETS question (3rd edition) page 119 #7 :

I had a problem solving the problem so I went straight to the explanation section,
It is hard to get the "step 2-3 " explanation.

How in step 2, the 2^29 + 2^29 later becomes in "step 3 " 2^30 ..


Please kindly explain. Thank you so much :)



greenlight-admin's picture

Hi Jenibae,

You'd like to know how/why 2^29 + 2^29 = 2^30
Good question.

Let's examine some similar examples:
x + x = 2x
k³ + k³ = 2k³
w² + w² = 2w²
7 + 7 = (2)(7)
135 + 135 = (2)(135)

Likewise, 2^29 + 2^29 = (2)(2^29)
= (2^1)(2^29)
= 2^30

Here's my step-by-step solution for that question: https://gre.myprepclub.com/forum/2-6286.html#p11148

Does that help?

Cheers,
Brent

Hi,

If a question has a condition such as xy ≠ 0 or xy > 0, then still x & y both can be negative no.
Since (negative)(negative)= Positive.

Just need a confirmation

greenlight-admin's picture

That's correct. If we're told that xy ≠ 0 or xy > 0, then x and/or y can still be either positive or negative.

For this question https://gre.myprepclub.com/forum/36a-25b-ab-3588.html for a fraction such as 25/36 i divided the numerator by 5 and denominator by 6 to get 5/6 and then picked C as the answer.Was my approach wrong because i divided the top and bottom by different numbers
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/36a-25b-ab-3588.html

To create equivalent fractions, we divide or multiply the numerator and denominator by the SAME value.

This is covered at 1:40 in the following video: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1065

Cheers,
Brent

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