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April 4th, 2018, 07:14 PM  #1 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0  Rational equation definition
Hi everyone, Stuck with this definition question. What is the meaning of a rational equation A) Two rational expressions having equal domains. B) The set of X values which satisfy two rational expressions. C) Two rational expressions which are equal to each other. D) Any equation having rational coefficients. I’m supposed to choose all the correct ones. Could be just one or maybe all 4 The more I read it, the more confused I get ! Thanks in advance! Last edited by Brunob; April 4th, 2018 at 07:18 PM. 
April 4th, 2018, 08:06 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,425 Thanks: 759  I don't think that's an official phrase I've heard used. It's the kind of thing that's most likely defined in your text prior to its use in the question. But if it does happen to be a standard phrase and I had to guess at its meaning, I'd reason like this. First, a rational expression is the ratio of two polynomials. A rational function is a rational expression interpreted as a function of some inputs, which can not include values that make the denominator zero. Then a rational equation must be a rational function equated to some value. Whether that value has to be a constant or whether it can be something else, depends on the context. For example $\frac{2x^2  5x + 3}{5x^3  3x^2 + 5x  6} = 47$ I would say is a rational equation. But can the right hand side be another rational function? Or perhaps some transcendental expression involving exotic functions? This all depends on what your text means by a rational equation. IMO, and I could be wrong, the phrase rational function or rational expression has a widely agreed on meaning as the ratio of polynomials; and the phrase rational equation does not have a standard meaning. 
April 4th, 2018, 08:22 PM  #3 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0 
I see what you mean! But on my material it doesn’t really answer or cover this question. Therefore I can’t really answer . I reasoned the way u did, but that got me nowhere to answer this question!
Last edited by Brunob; April 4th, 2018 at 08:26 PM. 
April 4th, 2018, 08:31 PM  #4  
Senior Member Joined: Aug 2012 Posts: 2,425 Thanks: 759  Quote:
Reasoning the way I do often gets me nowhere as well! What's the source of the question? Is it a text? Or some kind of standardized test? You know, looking at the alternatives given, C seems like the only correct solution. We have No, that doesn't sound right. Just because two rational expressions have equal domains, that doesn't give you an equation. Almost but not quite! If we have two rational expressions and set them equal, the values that satisfy the equation are the solution set. But the solution set itself isn't a rational equation, it's the set of solutions to a rational equation. So this is the answer designed to make you pick it incorrectly because it's almost right. That's the most sensible statement. Two rational expressions that are set equal to each other. That's the answer. It doesn't have to be just a constant on the RHS and it can't be something transcendental. Each side of the equation is a rational expression. It doesn't even make sense for an equation to have rational coefficients. They're trying to trip up the people who don't know the difference between an expression and an equation. Quote:
Hopefully you're now confused at a much higher level than you were before! Last edited by Maschke; April 4th, 2018 at 08:39 PM.  
April 4th, 2018, 08:35 PM  #5 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0 
it’s part of my homework. It’s not worth marks or anything ..I just wanna learn it because I have a test coming up.

April 4th, 2018, 08:37 PM  #6 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0 
Two rational expressions which are equal? Honestly I cannot figure it out lol . Stupid online math course

April 4th, 2018, 08:46 PM  #7 
Newbie Joined: Mar 2018 From: Canada Posts: 14 Thanks: 0 
Thank you so much! I was incline to exclude A and D from the start. But the more I read the more confused I got!

April 5th, 2018, 05:26 AM  #8 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
A "rational function" is a function that involves one or more fractions in which the numerators and denominators are polynomials. A "rational equation" is an equation that involves only rational functions. The "domain" of any function is the set of "x" values for which the operations defining the function can be performed. Since polynomials have domain "all numbers", the only restriction on rational functions is that "you cannot divide by 0". The domain of a rational function is all number except those that make a denominator 0. "X value" don't "satisfy" rational expressions. You must mean "rational equations". In that case x satisfies a given rational equation if and only if it makes both sides of the equation the same. Two rational expressions are "equal" if and only if they give the same values for all x. This is different from simply setting two rational expressions equal (so you have a rational equation) and asking what values of x make them equal. An expression having rational coefficients does not necessarily have anything to do with "rational expression". The coefficients of an equation are numbers so we are only asking that the coefficients be rational numbers (fractions). One important property of an equation with rational coefficients is that we can multiply the equation by the "least common denominator" of all the coefficients and convert to an equation with integer coefficients. 
April 5th, 2018, 06:09 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
You never told us Bruno: are you a student attending math classes?

April 5th, 2018, 06:52 AM  #10 
Senior Member Joined: Sep 2016 From: USA Posts: 683 Thanks: 456 Math Focus: Dynamical systems, analytic function theory, numerics 
To echo the other responses, the question itself is terrible. I don't know of any definition for the term "rational equation". However, I agree which Maschke that if I'm told that one of these answers must be correct, the only possible choice would be (c).


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