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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Simplify the following.

1/x-3 - 3(x-1)/ x^2-9

I have worked out this, but my final answer was different from what is at the back of the book.

The book has given the final answer as:

-2/x-3

The book did not provide the procedures, just the answer, please help.

Thanks in advance.

*Last edited by EbenezerSon (2013-07-08 08:58:29)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,847

Hi EbenezerSon

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Thanks, anonimnystefy.

But one thing left, I tried to use the SYMBOLS, I mean the mathematical symbols as you have used above nicely to solve the problem, but I couldn't locate where they were. Could you please assist me to find them and use them each time I want to post? The moderator, provided the link in my previous post, but I couldn't use them in this particular post.

Thanks. ;-)

*Last edited by EbenezerSon (2013-07-09 06:33:37)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,749

Hi;

Did you go to codecogs?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

No sir, I cannot even locate where they are!

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

hi EbenezerSon

The Latex editor is here:

http://latex.codecogs.com/editor.php

You can also type in what you want directly like this:

`[math]\frac{x^2 + 1}{x - 1}[/math]`

gives this:

and if you click on someone else's Latex you can see how they constructed it.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Please I need an assistance here:

Factorise the following expressions completely,

(1) (2m + 2k)^2 - (m - 2k)^2.

(2) ( x + 3)^2 - (x-7)^2.

(3) 9p^2 - (q^2 - 6qr + 9r^2).

(4) 4a^2 - 12ab - c^2 + 9b^2.

In each case the answer has been provided, but the procedures wasn't shown.

Thanks in advance.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

hi Ebenezerson

I think you'll need to multiply these brackets out like this

Then you can start to simplify.

Can you fill in the dots ?

Alternative way to do this:

**difference of two squares:**

Have you met this before ?

If so, you could put p = 2m + 2k and q = m - 2k

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Yes, with the difference of two square I have met that before.

But with respect to the first problem, my final answer was inconsistent with that of the book. But I I would try here.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

Shall I show you how I would do it?

It looks to me like you should do all the others using the difference of two squares.

But for (3) and (4), you'll have to work out what the two squares are.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

(2m + 3k)^2 - (m - 2k)^2

= (2m + 3k)(2m + 3k) - (m - 2k)(m - 2k)

= 4m^2 + 6km + 6km + 9k^2 - m^2 - 2km - 2km + 4k^2

=3m^2 + 8km + 13k^2.

That is it! How correct I am?

Thanks.

*Last edited by EbenezerSon (2013-07-10 07:58:36)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

= 4m^2 + 6mk + 6mk + 9k^2 - m^2 - 2km - 2km + 4k^2

There is a sign error here. The -2km terms must be subtracted so they become +

Bob

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

I see it the following:

Difference of two square: (p^2 - q^2) > I suppose it must be something like that in other to be called difference of two square, but I think something like (2m + 3k)^2 should be opened before manipulation, as I have done above.

Something like (q - p)^2 I think is not a difference of two squares. The book's final answer to the first question is (3m+ k)(m +5k). That really confuses me.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

Stay on-line and I'll show you both methods. It will take a few minutes to type up.

Bob

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

bob bundy wrote:

= 4m^2 + 6mk + 6mk + 9k^2 - m^2 - 2km - 2km + 4k^2

There is a sign error here. The -2km terms must be subtracted so they become +

Bob

Please I am not grasping what you mean could you demonstrate? Or you mean:

6km + 6km - 2km - 2km = 12km - 4km = 8km

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

OR by difference of two squares:

let p = 2m + 3k and q = m - 2k

I think the second way is quicker but either is OK

Bob

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Err sir I have understood you well! with (1) and (2). :-)

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

But please help me solve the third and the fourth ones.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

At first, I did not spot that this is the difference of two squares. But then I noticed that (q^2 - 6qr + 9r^2) is a perfect square:

So try this:

put P = 3p and Q = (q - 3r) and use

Bob

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

= (3p)^2 - (q- 3r)^2

= (3p - q - 3r)(3p +q - 3r).

Is that correct?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

That is so close to correct .... there is one - sign that should be a +

See if you can find it.

Bob

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Candidly speaking sir, I cant tell or explain why that negative sign should appear there, to be frank!

Whenever I am dealing with such complicated difference of two squares, positive and negative signs eludes me just in the end.

*Last edited by EbenezerSon (2013-07-10 08:40:55)*

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Please an assistance, please and why it should appear.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

put P = 3p and Q = (q - 3r) and use

so P+Q = 3p +(q-3r)

and P - Q = 3p - (q-3r)

When you remove the brackets the q becomes minus **and the -3r becomes +**

So can you see what the answer should be ?

Bob

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 230

Okay sir! but could you explain with an illustration, how you got the (q - 3r)^2 ?

In #19.

Thanks in advance.

*Last edited by EbenezerSon (2013-07-10 09:28:22)*

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