Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2013-07-09 06:57:54

EbenezerSon
Full Member

Offline

### Simplify the following:

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

Last edited by EbenezerSon (2013-07-09 06:58:29)

## #2 2013-07-09 07:30:57

anonimnystefy
Real Member

Offline

### Re: Simplify the following:

Hi EbenezerSon

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #3 2013-07-10 04:33:00

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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 (2013-07-10 04:33:37)

## #4 2013-07-10 04:56:51

bobbym

Online

### Re: Simplify the following:

Hi;

Did you go to codecogs?

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #5 2013-07-11 04:54:40

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

No sir, I cannot even locate where they are!

## #6 2013-07-11 05:05:23

bob bundy
Moderator

Online

### Re: Simplify the following:

hi EbenezerSon

The Latex editor is here:

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

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

#### Code:

$\frac{x^2 + 1}{x - 1}$

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

## #7 2013-07-11 05:09:21

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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.

## #8 2013-07-11 05:16:12

bob bundy
Moderator

Online

### Re: Simplify the following:

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

## #9 2013-07-11 05:23:23

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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.

## #10 2013-07-11 05:36:43

bob bundy
Moderator

Online

### Re: Simplify the following:

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

## #11 2013-07-11 05:39:31

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

(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 (2013-07-11 05:58:36)

## #12 2013-07-11 05:44:46

bob bundy
Moderator

Online

### Re: Simplify the following:

= 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

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

## #13 2013-07-11 05:51:45

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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.

## #14 2013-07-11 05:59:14

bob bundy
Moderator

Online

### Re: Simplify the following:

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

Bob

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

## #15 2013-07-11 06:01:48

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

#### 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

## #16 2013-07-11 06:06:57

bob bundy
Moderator

Online

### Re: Simplify the following:

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

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

## #17 2013-07-11 06:07:36

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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

EbenezerSon
Full Member

Offline

## #19 2013-07-11 06:18:58

bob bundy
Moderator

Online

### Re: Simplify the following:

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

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

## #20 2013-07-11 06:27:21

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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

Is that correct?

## #21 2013-07-11 06:28:46

bob bundy
Moderator

Online

### Re: Simplify the following:

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

See if you can find it.

Bob

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

## #22 2013-07-11 06:38:46

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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 (2013-07-11 06:40:55)

EbenezerSon
Full Member

Offline

## #24 2013-07-11 06:43:06

bob bundy
Moderator

Online

### Re: Simplify the following:

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

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

## #25 2013-07-11 06:50:26

EbenezerSon
Full Member

Offline

### Re: Simplify the following:

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

In #19.