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February 4th, 2014, 11:29 AM   #1
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Help me understand this step in an algebraic simplification?

I am using a book to brush up on some math, and there is a step in a problem that I do not understand.

I have a problem where I need to express the length of some rectangular fencing, P, as a function of one of the sides. If the sides are x and y, then the length of the fencing, P = 2x + 2y. I am given the area within the fence as 3600 sq. meters. Therefore, it is clear that xy = 3600 and y = 3600/x.

So, to express the length of the fencing P as a function of x, I should plug this value for y into the original equation for P, which is P = 2x + 2y.

This is 2x + 2(3600/x). All of these steps I can see on my own.

However, the book has the answer as

P = 2x + 2y
= x + 3600/x.

So my question is, how does 2x + 2(3600/x) simplify to x + 3600/x? Help appreciated!
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February 4th, 2014, 11:51 AM   #2
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Re: Help me understand this step in an algebraic simplificat

What you have there is right, P = 2x + 2(3600/x)...

Is there any other information it gives you. Can you to reference the book? The book sounds a little iffy
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February 4th, 2014, 12:06 PM   #3
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Re: Help me understand this step in an algebraic simplificat

Quote:
Originally Posted by SamSeymour

So my question is, how does 2x + 2(3600/x) simplify to x + 3600/x? Help appreciated!
It doesn't. And, it should be easy to convince yourself that it doesn't. If you ever doubt an equality, plug in some numbers!

Try x = 1:

2x + 2(3600/x) = 2 + 7200 = 7202

x + 3600/x = 1 + 3600 = 3601

In fact 2x + 2(3600/x) = 2(x + 3600/x)
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February 4th, 2014, 12:49 PM   #4
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Re: Help me understand this step in an algebraic simplificat

Ha! Well thank you then. I should have thought to plug in some numbers, but I will next time!

It is not a real book, but rather a written lecture from the math department of a university. Here are the two pages with this problem attached.
Attached Files
File Type: pdf Lecture 03(1).pdf (94.6 KB, 1 views)
File Type: pdf Lecture 03(2).pdf (23.5 KB, 3 views)
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