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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
When I got to (x² - 1)/x I
For the DS question here ( https://gmatclub.com/forum/if-xy-0-what-is-the-value-of-x-4-y-2-xy-2-x-3-y-283248.html ) the answer A was correct but had it been a PS I probably would have gotten it wrong. I ended up with (x+1)(x-1)/x, which evaluated to 3/2. However, your response to the questions evaluates to 5/2. Could you help me see what I miss, please?
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...
You did everything perfectly. It turns out that I don't know how to calculate 4-1 (-:
You're absolutely correct to say that the expression evaluates to be 3/2 (not 5/2)
I've edited my solution accordingly.
Thanks for the heads up!
Cheers,
Brent
Hi Brent
https://gmatclub.com/forum/if-x-1-2-then-6x-3-3x-2-8x-4-2x-322396.html
For the above question I plugged in the value as 1 and I yielded the ans D is there something that I am missing
Question link: https:/
Question link: https://gmatclub.com/forum/if-x-1-2-then-6x-3-3x-2-8x-4-2x-322396.html
When x = 1, the original expression evaluates to -1.
So for each answer choice, we'll replace x with 1 and evaluate each expression to get....
A) -3.5
B) 0.5
C) -1
D) -1
E) 7
Since A, B and E don't evaluate to -1 when x = 1, we can eliminate them.
This means we need to try another value of x.
When x = 2, the original expression evaluates to 8.
Now, for the remaining two answer choices (C and D), we'll replace x with 2 and evaluate each expression to get....
C) 8
D) 2
Since D doesn't evaluate to 8 when x = 2, we can eliminate it.
Answer: D
Does that help?
Hi Brent, yes this helps, but
Unfortunately, there's no
Unfortunately, there's no safe number that will always eliminate 4 of the 5 answer choices in 1 step.
That's the downside of testing numbers.