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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 437

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: 15,507

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: 437

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: 85,270

Hi;

Did you go to codecogs?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 437

No sir, I cannot even locate where they are!

I know only one thing - that is that I know nothing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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: 437

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.

I know only one thing - that is that I know nothing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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: 437

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: 6,335

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: 437

(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: 6,335

= 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: 437

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.

I know only one thing - that is that I know nothing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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: 437

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: 6,335

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: 437

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

I know only one thing - that is that I know nothing

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 437

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

I know only one thing - that is that I know nothing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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: 437

= (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: 6,335

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: 437

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: 437

Please an assistance, please and why it should appear.

I know only one thing - that is that I know nothing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,335

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: 437

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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