Exponents and fractions - stuck on correct method  TOPIC_SOLVED

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Exponents and fractions - stuck on correct method

Postby Szechuan on Thu Aug 04, 2011 7:57 pm

Greetings,

I am about to enter an Engineering program after several years out of school. I took high-school calculus ten years ago but I was not a good student and mainly coasted through the work. I had decent marks (80+) but no retention of the theory.

The university has provided me with a 50-page booklet to help brush up on my math skills but I am having some difficulty as I am almost starting from scratch. This site has been a huge help so far but there is one problem I can't figure out and cannot find anything analogous to it in the guides.

I need to simplify the following equation:

( ( y / x ) + x) / ( 2 / x )

The solution at the back of the book is: ( y - x^2 )/2

My workflow is as follows:

1. ( ( y / x ) + x) / ( 2 / x )

2. Multiply by x^-1 (or 1/x):

<( ( y / x ) + x) / ( 2 / x )> * (x^-1)

3. Which results in:

(y + x(x^-1)) / 2

And this is where I am stuck. Every attempt I make to get past this just turns the whole thing into a disorganized mess and it is clear I am overlooking something important. I don't understand how to treat the x(x^-1) nor do I understand how the solution converts "y + x" to "y - x". I've been able to work backwards from the solution for the other questions I did incorrectly and figure out where I went wrong, but I am having no luck here.

I don't even understand what kind of equation this is so I have been unable to find any examples. I hope this is in the right place and I hope somebody can help me out!
Szechuan
 
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Postby stapel_eliz on Thu Aug 04, 2011 8:00 pm

Szechuan wrote:I need to simplify the following equation:

( ( y / x ) + x) / ( 2 / x )

Since there is no "equals" sign, this is not an equation; it's just an expression.

Szechuan wrote:2. Multiply by x^-1 (or 1/x):

<( ( y / x ) + x) / ( 2 / x )> * (x^-1)

You can only "multiply through" when you have two "sides" (of an equation). Otherwise, you are changing the expression.

To learn how to simplify "complex" fractions, please try this lesson. :wink:
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Re: Exponents and fractions - stuck on correct method

Postby Szechuan on Thu Aug 04, 2011 9:03 pm

Thanks a ton, I had no idea how to get through that! Evidently my ignorance is greater than I thought...
Szechuan
 
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Re: Exponents and fractions - stuck on correct method

Postby Szechuan on Thu Aug 04, 2011 10:57 pm

I have tried the steps indicated on the site, and am getting closer to the answer. But I still cannot figure out where the minus sign is coming from! There are no negatives whatsoever in the expression so I don't understand how this is happening.

Current Attempt:

1. ((y/x)+ x) / (2/x)

2. Find common denominators: ((y+x^2)/x ) / (2/x)

3. Flip and multiply: ((y + x^2) / x ) * ( x / 2 )

Which should result in (y + x^2) / 2 shouldn't it?
Szechuan
 
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  TOPIC_SOLVED

Postby stapel_eliz on Fri Aug 05, 2011 12:50 am

Szechuan wrote:I still cannot figure out where the minus sign is coming from!

I hadn't even noticed that. Yes, you're right: there is no reason for the "minus" sign. Oops! :wink:

You might want to point out the error to your school. You're probably not the only person who's been confused by their mistake. :shock:
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Re: Exponents and fractions - stuck on correct method

Postby Szechuan on Fri Aug 05, 2011 1:13 am

Haha, that certainly explains that! I was tearing my hair out trying to figure out what the heck was wrong. I've even had my roommate come verify the question and answer (without telling them what I thought it was) to make sure I hadn't misread it or something.

Thanks again for the help!
Szechuan
 
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