Algebra Book, pg 112, #13

[jcraft111]

I understand how to do the problem, but I have no idea how to simplify the answer. I don't understand the last two lines of the solution that can be found at the bottom of pg 114. More specifically, I really don't understand the part that states: = 1 over x squared minus 1 over x + 1 over x. I am completely lost there...

Any help you can provide would be greatly appreciated.

[tommywallach]

Hey Jcraft,

I can explain!

1/x + 1 = 1/x + x/x

Now that you have a common denominator, you can just add the numerators:

1 + x / x

Make sense?

-t

P.S. I changed it, but in the future, if you have a question, please put the name of the book, as opposed to the number. Thanks! : )

[nealont1]

Tommy,
Even with this clarification I'm still unsure of how to solve the problem. I understand that x/x = 1. But could you break down the solution to this one step by step? The book explanation is leaving me with more questions than answers.

[tommywallach]

Hey Nealont,

Here's what you need to remember: the only way to combine fractions is to create common denominators. If there's ever a step in the solution that confuses you, focus on how they created a common denominator. For example, if you have:

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

The only common denominator you can create here is x^2 * (x + 1). This happens a couple times in the solution, but everything else is fairly straightforward. If there are specific steps that confuse you, let me know them, otherwise, the solution is already very complete in the book (and better than I can make it here, where I'd have to do division symbols and carat symbols, instead of the much more elegant one with bar lines for fractions and actual exponents!).

-t