simplify rational: (3x-12/x)/(x-2/3/(x+1))

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jomcan

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I can not get this question to resolve to the answer in the book.

(3x-12/x)/(x-2/3/(x+1))
 
What does "x- 2/3/(x- 1)" mean"? Since division is not "associative" this could be interpreted as "(x- 2/3)/(x- 1)" or as "x- 2/(3/(x- 1))" and those are not the same.
 
jomcan said:
I can not get this question to resolve to the answer in the book.

(3x-12/x)/(x-2/3/(x+1))
Click to expand...
Does your problem look like

\(\displaystyle \displaystyle{\dfrac{{3x - \dfrac{12}{x}}}{{x - \dfrac{2}{\left (\dfrac{3}{x+1}\right )}}}}\)
 
S Khan

Yes! except for the parenthesis in the denominator. I included them for thoroughness because i could not draw the question. The question is like a triple sandwich 2 over 3 over x+1.

I get from 3x-12/x =(3x^2 - 12) / x for numerator and my first step at denom is x-2/3/x+1 = x -2/(3x+3) then 3x^2 + 3x - 2 all over 3x+3 and this may be where i am making an error. HallsofIvy points out that 2/3/(x+1) can be interpreted several ways but my understanding is there is always a right way and only that right way to interpret an order of operations.

then: 3x^2-12/x all over 3x^2 + 3x -2 / 3x+3

then:[ 3 (x+2) (x-2)]/x all over [3x^2 + 3x -2] /[ 3 (x+1)] where i would expect [3x^2 + 3x -2] to factor into cancel-able terms.
 
jomcan said:
I get from 3x-12/x =(3x^2 - 12) / x for numerator...
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Yes.

jomcan said:
...and my first step at denom is x-2/3/x+1 ...
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No; "x-2/3/x+1" has no fixed meaning. To type this out as text, using grouping symbols:

. . . . .x - 2/[3/(x + 1)]

jomcan said:
= x -2/(3x+3)...
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No; since 3 divided by x + 1 is not equal to 3 multiplied by x + 1, it cannot be true that 3/(x + 1) is equal to 3(x + 1) = 3x + 3. Instead, try doing the fraction division by flipping and multiplying:

. . . . .2/[3/(x + 1)] = (2/1)*[(x + 1)/3]

Simplify. ;)
 
Subhotosh Khan said:
Does your problem look like

\(\displaystyle \displaystyle{\dfrac{3x - \dfrac{12}{x}}{{x - \dfrac{2}{\left (\dfrac{3}{x+1}\right )}}}}\)
Click to expand...

Jomcan,

For your interpretation to be correct - the expression needs to be:

\(\displaystyle \displaystyle{\dfrac{3x - \dfrac{12}{x}}{x - \dfrac{\frac{2}{3}}{(x+1)}}}\)

Is this the correct one?
 
simplify rational

The answer in the text is 9(x+2)/2. I will try the advices that I have been given and see if I can get to that.
 
rational

replying to S. Kahn: Your second drawing of the question is closer, but the q. as posited in the text has no parenthesis. My guess is now that it is a poorly constructed question that was not caught by the proof reader. If the question is printed wrong the answer may very well not be correct. You see, I saw this question yesterday when i was working as a substitute teacher. the curriculum keeps changing around here way too often and we get new texts as well. I think this is just some "rushed to print" material.

Tried it again and now I get [9(x-2)]/x
 
.2/[3/(x + 1)] = (2/1)*[(x + 1)/3] this makes more sense. I was trying to do 2/3 all over (x+1)/1 . I was guessing the implied "1" could be placed under the (x+1).


. . . . .




. . . .
 
The "order of operations", sometimes remembered as "Please Excuse My Dear Aunt Sally", gives the precedence as "Parentheses", "Exponentation", "Multiplication", "Addition", and "Subtraction". It does not say which division is to be done first when you have several divisions! As I said before a/b/c can be interpreted as (a/b)/c or as a/(b/c) and those are NOT the same. The first, (a/b)/c is the same as a/(bc) while the second is (ac)/b.
 
HallsofIvy said:
The "order of operations", sometimes remembered as "Please Excuse My Dear Aunt Sally", gives the precedence as "Parentheses", "Exponentation",
"Multiplication", "Addition", and "Subtraction".
It does not say which division is to be done first when you have several divisions! <----- That is incorrect.
As I said before a/b/c can be interpreted as (a/b)/c or as a/(b/c) and those are NOT the same. The first, (a/b)/c is the same as a/(bc) while the second is (ac)/b.
Click to expand...

No, that is incorrect.

When written as "a/b/c," the divisions are performed from left to right, even if they are adjacent to each other.

a/b/c is not equivalent to \(\displaystyle \ \dfrac{\dfrac{ \ \ \ a \ \ \ }{b}}{c}, \ \ \) the latter being ambiguous. But, as we are not given a form of the latter when it is written

in the horizontal style, it is irrelevant.

A good example of a/b/c is 12/6/2.

It unambiguously equals 1.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - --


jomcan said:
I can not get this question to resolve to the answer in the book.

(3x-12/x)/(x-2/3/(x+1))
Click to expand...

And, jomcan, your expression is incorrect for it to lead to the answer in the book.

It needs grouping symbols, such as:

(3x - 12/x)/[x - 2/(3/(x+1))], because the incorrect

2/3/(x + 1) means \(\displaystyle \ \dfrac{(\tfrac{2}{3})}{x + 1} \ = \ \dfrac{2}{3(x + 1)} \ = \ \dfrac{2}{3x + 3}.\)
 
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could the ambiguity be cleared up

lookagain said:
No, that is incorrect.

When written as "a/b/c," the divisions are performed from left to right, even if they are adjacent to each other.

a/b/c is not equivalent to \(\displaystyle \ \dfrac{\dfrac{ \ \ \ a \ \ \ }{b}}{c}, \ \ \) the latter being ambiguous. But, as we are not given a form of the latter when it is written

in the horizontal style, it is irrelevant.

A good example of a/b/c is 12/6/2.

It unambiguously equals 1.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - --




And, jomcan, your expression is incorrect for it to lead to the answer in the book.

It needs grouping symbols, such as:

(3x - 12/x)/[x - 2/(3/(x+1))], because the incorrect

2/3/(x + 1) means \(\displaystyle \ \dfrac{(\tfrac{2}{3})}{x + 1} \ = \ \dfrac{2}{3(x + 1)} \ = \ \dfrac{2}{3x + 3}.\)
Click to expand...


Could the ambiguity be cleared up by using different length of line to indicate division in the vertical presentation of the question?
 
jomcan said:
Could the ambiguity be cleared up by using different length of line to indicate division in the vertical presentation of the question?
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Use of parentheses is the preferred way (although redundant)

so:

a/b/c = (a/b)/c ..... the RHS (with redundant parentheses) is clearer.
 
jomcan said:
Could the ambiguity be cleared up by using different length of line to indicate division in the vertical presentation of the question?
Click to expand...
That's how it's usually done, with professional typesetting. However, the software that controls the relative lengths of those fraction bars sometimes sets the two lengths too close to one another (i.e., not programmed by a mathematician).

Maybe the fraction bars in your text are already different lengths, but you need a magnifying glass to discern it. (This has been an issue for me, before.) :cool:
 
The answer in the text is 9(x+2)/2 (NOT)

"Are you sure the book shows a 2 as the denominator? " No. Checked yesterday and it is indeed x for denominator. But cannot discern any length difference in fraction bars.
 
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