Variable

[Lolastarr]

True or false, When a variable is a part of
two different fractions with
two different denominators,
you must multiply everything
on both sides of the
equations by the denominator
of the left-most fraction.

 

[pka]

True or false, When a variable is a part of
two different fractions with
two different denominators,
you must multiply everything
on both sides of the
equations by the denominator
of the left-most fraction.

I cannot imagine how a nonsense statement can be either true or false.

 

[Lolastarr]

I cannot imagine how a nonsense statement can be either true or false.

This is how the question is written in the math book

 

[Otis]

This is how the question is written in the math book

Hi Lolastarr. Are you sure that you've posted all the given information (eg: instructions; references, method)?

I can contrive situations for which the statement is not true. Whether those situations have anything to do with your studies or assignment, I can't say.

?

 

[Dr.Peterson]

True or false, When a variable is a part of
two different fractions with
two different denominators,
you must multiply everything
on both sides of the
equations by the denominator
of the left-most fraction.

Anything that says "to solve ___, you MUST do ___" is inherently false. There are always alternative things you CAN do, even if they might not be the most efficient.

And the statement here is so general (where is x? in a denominator or not? in one place or not?) that even if it were true, I wouldn't know what that meant.

I'd have to see the whole chapter in the book in order to judge whether what they say makes any sense in context.

 

[JeffM]

I can see a context in which it may be at least sane to ask this as a true-false question, namely in the context of clearing fractions, but then why post it in calculus. Surely someone studying calculus knows how and when to clear fractions.

If someone writes a cookbook type of text on beginning algebra, they might say of fractional coefficients of the unknowns:

To clear fractions, multiply both sides of the equation by the denominator with the largest absolute value and simplify, then do the same thing with the denominator of next largest absolute value remaining and simplify, and keep on doing that until there are no fractions left.

It is not so efficient a method as multiplying both sides of the equation by the least common multiple, but it will work. And finding the least common multiple may involve a fair amount of work on its own.

In that context, the problem calls for an answer of "false" and has some motivation. I still think it is quite foolish, and obviously foolish problems can perplex students. I'd love to know what the context of the problem is.