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# Applications of Rational Expressions

Posted on 2004-08-31
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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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Question by:mvibe
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Expert Comment

ID: 11946477
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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Expert Comment

ID: 11946878
a = PL / Ee
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Expert Comment

ID: 11947968
This reminds me of that Ogden Nash verse entitled "On The Antiquity of the Microbe" : Adam Had'em
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Expert Comment

ID: 11947974
Both 'a' and 'e' must be non-zero for the equation to have meaning
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Expert Comment

ID: 11947993
dhsindy,
Unless either P or L are zero too, in which case 'a' could be anything.
JR
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Expert Comment

ID: 11949064
>> 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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Expert Comment

ID: 11950033
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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Expert Comment

ID: 11950173
>> 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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Expert Comment

ID: 11953257
avizit,
You are just plain and simple wrong!
JR
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Expert Comment

ID: 11953525
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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Expert Comment

ID: 11953583
>> 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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Expert Comment

ID: 11953655
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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Expert Comment

ID: 11954432
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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Expert Comment

ID: 11954530
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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Expert Comment

ID: 11954558
>>but what do you really think it is at zero?

we say it is undefined.
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Expert Comment

ID: 11954568
okay d-glitch is faster :) '

and thanks rjkimble :)
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Expert Comment

ID: 11954712
>>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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Expert Comment

ID: 11954922
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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Expert Comment

ID: 11955071
ok, what is the slope of the curve (the differential) of sin(x)/x at x = 0?
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Expert Comment

ID: 11955631
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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Expert Comment

ID: 11955829
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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Author Comment

ID: 11956040
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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Accepted Solution

d-glitch earned 250 total points
ID: 11956504
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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Expert Comment

ID: 11956645
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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Author Comment

ID: 11957434
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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