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Comment on Simplify Rational Expression
why did you take the factor
You can only can only cancel
You can only can only cancel expressions that are "multiplicands" (part of some product). For more, see https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...
You cannot cancel out "summands." Take (9+1)/(9+2) for example. We can't cancel the 9's to get 1/2
Sometimes you learn exactly
However, I notice the video you link to does not explicitly mention summands and multiplicands. Is there any resource that you know of which covers these rules and common errors when simplifying?
Good point. I'll check around
Good point. I'll check around.
We could also see that as x
The only answer choice that behaves in the is the some way is D)
Nice approach!
Nice approach!
That sounds like a nice
When we say that [98x^5 - 8x
When we say that [98x^5 - 8x^3]/[98x^5 + 56x^4 + 8x^3] = (7x - 2)/(7x + 2) for all values of x, this means that, if replace x with any value, both expressions will evaluate to the same value.
For example, let's see what happens when x = 1
So, replace x with 1 to get:
[98(1^5) - 8(1^3)]/[98(1^5) + 56(1^4) + 8(1^3)] = [7(1) - 2]/[7(1) + 2]
Simplify: [98 - 8]/[98 + 56 + 8] = [7 - 2]/[7 + 2]
Evaluate: 90/162 = 5/9
Perfect! It's true that 90/162 = 5/9
What Aurian has done is replace x with a super big number and make an observation about the value of the expression [98x^5 - 8x^3]/[98x^5 + 56x^4 + 8x^3]
For example, let's say that we replace x with 1,000,000
When we do so, x^5 becomes SUPER HUGE. In fact, x^5 is so large, the other parts of the expression have very little impact on the value of the expression (in comparison to x^5)
So, when we replace x with 1,000,000, the expression [98x^5 - 8x^3]/[98x^5 + 56x^4 + 8x^3] ≈ [98x^5]/[98x^5] ≈ 1
When we take each answer choice, and replace x with 1,000,000 only answer choice D evaluates to be a number very close to 1.
That is, (7x - 2)/(7x + 2) ≈ 7x/7x ≈ 1
Hi,
I used this approach & got the correct answer
I used X = 1 (random number) into the main eqn
& got the result as 0.55
Then for all the 4 option used X = 1 & checked the result only in option D Value was 0.55
So will this approach work for all such question
PLs help
Perfect approach!
Perfect approach!
Yes, that strategy will work for all questions of this nature.
Cheers,
Brent
Why does D not simplify
In order to simplify a
In order to simplify a fraction, we must divide numerator and denominator by the same value.
Take, for example: 24/36
We can divide numerator and denominator by 12 to get the EQUIVALENT (and simplified) fraction 2/3
Likewise, to simplify (7x - 2)/(7x + 2), we must divide numerator and denominator by the same value.
In this case, what would we divide by? We don't have any useful options.
So, we can say that (7x - 2)/(7x + 2) is written in simplest form.
For more on simplifying fractions, watch: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1065
Cheers,
Brent
Hi Brent, so in this question
To better understand why we
To better understand why we can't just cancel 98x^5 from the numerator and the denominator, let's examine a similar case.
Let's say we have the following fraction: (10 + 1)/(10 + 2)
Although we have 10 in both the numerator and denominator, we can't "cancel them" to get 1/2
As you can see, (10 + 1)/(10 + 2) and 1/2 are not equivalent fractions.
Now consider a different fraction: (10)(1)/(10)(2)
We can rewrite this fraction as: (10/10)(1/2)
Then simplify to get: (1)(1/2), which is equal to 1/2
You might want to review this lesson on simplifying rational expressions: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...
Hi Brent, not sure what's
What is the ratio of the product (20!) (16!) to the product (22!) (14!) ?
A 1 to 2
B 40 to 77
C 8 to 11
D 1 to 1
E 80 to 70
(20!) (16!)/(22!) (14!)
14! (6! 2!)/ 14! (8! 1!) Factor out 14! and it cancel out
1!/2!
1/2
There are two big problems
There are two big problems with your solution:
First, 14! x 6! ≠ 20!
(14!)(6!) = [(14)(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)][(6)(5)(4)(3)(2)(1)]
Whereas 20! = (20)(19)(18)(17)(16)(15)(14)(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
Second, the type of factoring you are doing, applies only to algebraic expressions separated by addition and subtraction.
For example 3x + 12 = 3(x + 4)
When it comes to multiplication, we can't use the same kind of factoring.
For example, (3)(6)(9) ≠ 3(2)(3)
Here's my solution:
You we want to find the simplified value of (20!)(16!)/(22!)(14!)
Notice that 16! = (16)(15)(14!)
And 22! = (22)(21)(20!)
So we can rewrite our ratio as: (20!)(16)(15)(14!)/(22)(21)(20!)(14!)
Cancel the 20!'s to get: (16)(15)(14!)/(22)(21)(14!)
Cancel the 14!'s to get: (16)(15)/(22)(21)
Prime factorize numerator and denominator: (2)(2)(2)(2)(3)(5)/(2)(11)(3)(7)
Simplify: (2)(2)(2)(5)/(11)(7)
Evaluate: 40/77, which is the same as 40 to 77
Answer: B
Ah make sense.
Noted for the facotring rule and thanks Brent.