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Applications of Rational Expressions

There seems to be quite a few formulas that outline how to solve rational expression equations, but none that I have read about so far really make it any easier to understand.

Ex.     Solve for the variable (a)

         E = PL / ae

Is there a formula and easily understood explanation to the above problem?
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mvibe
Asked:
mvibe
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1 Solution
 
d-glitchCommented:
Good tutorial on rational expressions here:     http://www.purplemath.com/modules/rtnldefs.htm

But I'm afraid I don't understand your equation at all.  What are E PL a and e  ???
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ozoCommented:
a = PL / Ee
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JR2003Commented:
This reminds me of that Ogden Nash verse entitled "On The Antiquity of the Microbe" : Adam Had'em
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dhsindyRetiredCommented:
Both 'a' and 'e' must be non-zero for the equation to have meaning
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JR2003Commented:
dhsindy,
Unless either P or L are zero too, in which case 'a' could be anything.
JR
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rjkimbleCommented:
>> dhsindy,
>> Unless either P or L are zero too, in which case 'a' could be anything.
>> JR

Not true -- dhsindy's comment is accurate. You can't divide by 0 -- end of story.
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JR2003Commented:
rjkimble,

>>>Not true -- dhsindy's comment is accurate. You can't divide by 0 -- end of story.

It depends which zero it is. For example if you have and expression like something like x/x or say x/sin(x) then at zero the result is 1. Even though you are dividing zero by zero. So not quite end of story. This is because in problems like this you look at the limit of the expression as x tends to zero.
JR
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avizitCommented:
>> x/sin(x) then at zero the result is 1

No,  1 the limit the expression tends to when x tends to zero . 1 is  NOT the value of the expression at x = 0.



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JR2003Commented:
avizit,
You are just plain and simple wrong!
JR
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d-glitchCommented:
The function  x/sin(x) has a Removable Singularity at x=0:                       http://mathworld.wolfram.com/RemovableSingularity.html
But it is still undefined at that point.

You may be able to make a new analytic function by evaluating                http://mathworld.wolfram.com/RiemannRemovableSingularityTheorem.html
the limit of the original function at the singularity.  
But it is a new function.  

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rjkimbleCommented:
>> It depends which zero it is. For example if you have and expression like something like x/x or say x/sin(x) then at zero the result is 1.

You are confusing division by zero with the limit of an expression as the divisor approaches zero. They are not the same thing. As I indicated before, you cannot divide by zero -- there are no conditions which allow you to do so. Sorry, but you're the one who is just plain wrong.

Furthermore, avizit is exactly right, plain and simple.
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avizitCommented:
okay yuo have to understand that the

limit of a function F(x) as x tends to zero is NOT
the same as the VALUE of the function when x IS 0

-------------
now ..,the limit x->0  sinx/x  exists and is = 1

but  the value sin(x)/x  at x = 0 is undefined.

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JR2003Commented:
ok, thank you for correcting me.
I know you say it's undefined but what do you really think it is at zero?
Are we just picking hairs here?
And what would x/x be at x = 0. Surely that must be 1?
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d-glitchCommented:
Mathematicians take singularities very seriously.  They have to.  

                  http://www.experts-exchange.com/Miscellaneous/Math_Science/Q_21095753.html

The value of x/x at x=0 is undefined.
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avizitCommented:
>>but what do you really think it is at zero?


we say it is undefined.
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avizitCommented:
okay d-glitch is faster :) '

and thanks rjkimble :)
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avizitCommented:
>>And what would x/x be at x = 0. Surely that must be 1?



then you can have two lines of thought, both wrong

1>. you can say any number divided by itself = 1

          2/2 is 1 , 3/3 is 1 and so 0/0 is one

2>. you can also say , zero divided by any number is 0

          0/2 is 0 , 0/9 is 0 . 0/87378648764 is 0 so 0/0 is 0




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gilbarCommented:
now you made me jump in!

0/0 = R  where R is all real numbers. thus
R*0 = 0  and
0*R = 0  
see? the result of  dividing by zero IS defined, as undetermined.
OH! you're using your own math (where division by zero is undefined) not using mine. You all do know there's not just one math don't you?
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JR2003Commented:
ok, what is the slope of the curve (the differential) of sin(x)/x at x = 0?
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JR2003Commented:
Ok, so if you apply L'Hopital's rule you can remove the singularity and then sin(x)/x is 1 when x = 0.
As it's a removable singularity I just removed it as the expression would suggest I could.
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d-glitchCommented:
Hello mvibe,

This is your first question on EE.  Things will work out better if you stay involved with the question, and post your concerns and comments here rather than in the Member Feedback section.

                   >>  Doesn't know formulas for Applications of Rational Expressions:
                         Such as
                         Distance, Rate, and Time -> D/T=R for T

I assure you I do understand formulae.  

Do you understand that "Rational Expression" has a particular mathematical connotiation -- and I gave you a link to its definition.

If     E = PL / ae    is just a formula like      D/T=R     and you don't know what    E PL a and e  stand for,
then you should say so here so everyone can see it and we can all get back on track.
 
 
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mvibeAuthor Commented:
d-glitch,

My apologies. Being new to this forum, I was mistaken in thinking that by replying to my own question it would cost me more points. I ask the original question the only way I know how ... this question was one I was given in a recent final exam and I could not answer because of the lack of experience and pure hatred I have for this sort of math. Can I take back or make good on my Feedback in any way?

Let me outline how the instructions were given to me from my text book along with a second example, so maybe my question will make more sense.

     "Solve each formula for the indicated variable"
      P = A/C+D <- Solve for A

And example given to us in the book uses the Distance, Rate, and Time formula and I think that is where I get lost. The chapter in the text book is titled:     "Rational Expressions: Applications of Rational Expressions"

Let me know if this makes more sense?

Jeff
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d-glitchCommented:
I'm not worried about my feedback in this case.

ozo's post is the correct answer to your original question.

The general method of solution goes something like this:      If you have an equation, then both sides are equal.

                                                                                       You can perform the same operation on each side and maintain the equality.
                                                                                        This includes addition, subtraction, multiplication, and division.
                                                                                        But not division by zero.

                                                                                        So do what you have to do perform operations to isolate the variable of interest.


                                                        Question 1:                Solve          E = PL / ae              for a

                                                                                         Multiply each side by a                  ==>     Ea    = PLa/ae
                                                                                         Cancel the a's on the right side      ==>     Ea    = PL/e
                                                                                         Divide each side by E                    ==>     Ea/E = PL/Ee
                                                                                         Cancel the E's on the left side        ==>     a     = PL/Ee


                                                       Question 2:                Solve           P = A/C+D                for A

                                                                                        Subtract D from each side              ==>    P-D       = A/C+D - D
                                                                                        Cancel the D's on the right             ==>     P-D      = A/C
                                                                                        Multiply both sides by C                  ==>    C(P-D)  = CA/C
                                                                                        Cancel the C's on the right             ==>    C(P-D)  = A

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JR2003Commented:
I should take my discussion elsewhere as it's of no benefit to mvibe. New question posted at:
http://www.experts-exchange.com/Miscellaneous/Math_Science/Q_21115733.html
for 500 points.
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mvibeAuthor Commented:
Thank-you ozo for the correct answer and d-glitch for the explanation I was looking for. Plain English step-by-step.
I kept getting turned around at the "divide each side by E" part.

mvibe
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