Exponents and fractions - stuck on correct method

[Szechuan]

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!

[stapel_eliz]

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.

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.

[Szechuan]

Thanks a ton, I had no idea how to get through that! Evidently my ignorance is greater than I thought...

[Szechuan]

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?

[stapel_eliz]

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!

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.

[Szechuan]

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!