Simplify (x^2-y^2)/(x^2+4xy+3y^2)*(x^2+xy-6y^2)/(x^2+xy-2y^2)

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Dirty.Rotten.Imbecile

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What do you think about this one? The answer is dissatisfying, there's no way to test it and the text book has the incorrect answer in the solutions section.

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Dirty.Rotten.Imbecile said:
I tried that and found that the equation is equal to one half.
Click to expand...
You meant to type "negative one half", yes?


I tried again using 4 and 6 I shoulda used two other numbers.
Click to expand...
Actually, you ought to have used a pair of xy-values such that the ratio y/x is not proportional to 3/2. But, you didn't realize that.

Your work is correct, except for the last step.

The given product simplifies to (x - 2y)/(x + 2y).

In your last step, you concluded that this expression equals -1. That was a false assumption.

Perhaps, you focused on just -(2y)/(2y) and saw "-1". It doesn't work that way because adding x affects the value of both the numerator and the denominator. (Remember the Order of Operations.) That is, after adding some non-zero x on top and bottom, there is no more "-2y/2y".

It can be shown that (x - 2y)/(x + 2y) = -1/2 whenever the ratio y/x = 3/2.

Denis suggested x=2 and y=3; then you coincidentally picked x=4 and y=6 -- another pair where y/x=3/2. A lesson here is: always conduct a variety of trials, before drawing a conclusion. :cool:

The answer to your exercise is simply (x - 2y)/(x + 2y).
 
Last edited:
mmm4444bot said:
You meant to type "negative one half", yes?


Actually, you ought to have used a pair of xy-values such that the ratio y/x is not proportional to 3/2. But, you didn't realize that.

Your work is correct, except for the last step.

The given product simplifies to (x - 2y)/(x + 2y).

In your last step, you concluded that this expression equals -1. That was a false assumption.

Perhaps, you focused on just -(2y)/(2y) and saw "-1". It doesn't work that way because adding x affects the value of both the numerator and the denominator. (Remember the Order of Operations.) That is, after adding x on top and bottom, there is no more "-2y/2y".

It can be shown that (x - 2y)/(x + 2y) = -1/2 whenever the ratio y/x = 3/2.

Denis suggested x=2 and y=3; then you coincidentally picked x=4 and y=6 -- another pair where y/x=3/2. A lesson here is: always conduct a variety of trials, before drawing a conclusion. :cool:

The answer to your exercise is simply (x - 2y)/(x + 2y).
Click to expand...

ok that's great!

So I have noticed this before. When I have a rational expression in which the same value appears in both numerator and denominator I'm not supposed to cancel it out but in this case I cancelled out the x in the numerator and the x in the denominator which left a negative value divided by its positive value which is -1. I must remember to remember that.?
 
PS: In the future, please start new threads for new exercises. Thanks. :cool:
 
Dirty.Rotten.Imbecile said:
When I have a rational expression in which the same value appears in both numerator and denominator I'm not supposed to cancel it out ...
Click to expand...
You may cancel identical objects in the numerator and denominator IF they are both factors.

In the expression (x - 2y)/(x + 2y), the symbol x is not a factor; it's an addend.

Factors would look something like this:

x(-2y)/[x(2y)] = -1
 
mmm4444bot said:
You may cancel identical objects in the numerator and denominator IF they are both factors.

In the expression (x - 2y)/(x + 2y), the symbol x is not a factor; it's an addend.

Factors would look something like this:

x(-2y)/[x(2y)] = -1
Click to expand...
Gotcha! Thanks. You are an officer and a gentlemen.?
 
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