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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Hello everyone! Please help me to continue solving this equation:

-7((1/x)-1)=4+2((1/x)-1)^2

Here's what I did:

I let w= (1/x)-1

So I have:

-7w=4+2w^2

2w^2+7w+4=0

Then I factored it using quadratic equation so I've got:

w= (-7±√17)/4 *Note: √17 is square root of 17.

Since w= (1/x)-1

(1/x)-1= (-7+√17)/4 and (1/x)-1= (-7-√17)/4

I find it hard to evaluate the value of x from the 2 equations I've got. Maybe I've done something wrong in simplifying these 2 or much worse,my entire solution is wrong.So please help me find the way out. I'm also looking for other way to solve it. If someone out there know it, kindly share it to me. I would be very grateful for someone who'd help. I'd be waiting for replies then! Have a nice day!:D

*Last edited by 295Ja (2012-12-02 23:41:54)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi 295Ja

Welcome to the forum!

That method is the one I would have chosen and you have done it correctly.

Alternatively you could substitute y = 1/x and make a quadratic in y. It would be more complicated because you'd have to expand the bracket squared.

Or you could clear the brackets from the original, (more complicated) then times by x^2 to clear the fractions. Again, more steps.

You can rearrange your answer like this:

so

I've checked these in the original and both work ok.

Hope that helps!

Bob

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

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Bob thank you for helping! I hope you won't mind if I'll visit this forum more often and post problems I'll find confusing in the future.

May I just ask for one clarification? I remember my teacher told us that we must avoid doing cross multiplication

when there is a variable involve. But I just noticed that to arrive on the answer to my question, x must be cross multiply to -3±√ 17. If I'll just state on my solution that x≠0, will it be allright to do a cross-multiplication?

*Last edited by 295Ja (2012-12-02 23:44:45)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Hi 295Ja;

Welcome to the forum.

I think you are mistaking the term cross multiplying for division. You may never divide by 0 unless it is stated in the problem that x ≠ 0.

So if a variable might be 0 you should not divide by it. In this case from the formulation of the problem you can see that they are saying x ≠ 0.

I hope you won't mind if I'll visit this forum more often and post problems I'll find confusing in the future.

That is the purpose of the forum. It is a place where like minds can freely share information.

**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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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Thank you for clarifying that to me!

I'm just curious, what is now the time at your place? By the way, I'm from the Philippines and its now 5:55 pm here.:D

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Hi;

It is 2:55 AM here.

**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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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

Whooh! I admire you for being awake this time around knowing that it's an early morning there.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Do not admire me. I do not require much sleep and am capable of going without any for 36 hours or so.

**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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi 295Ja

Here is an example where 'cross-multiplying' has been done incorrectly.

Student remembers about cross multiplying, but does it incorrectly:

It is because of this sort of mistake that teachers advise against using cross multiplication.

I prefer to teach 'multiply every term by the same amount', so in the above example:

Another thing you may find helpful is to convert the algebra to numbers.

In my example, suppose u = 3, v = 6 and f = 2

In the original:

This is correct.

In the error version:

This is NOT CORRECT so the error is revealed.

In my correct version:

This has come out correctly.

This is not a guarantee that no mistake has been made as I might just have been lucky to get the 'right answer', but it will help to confirm that what you have done is right.

It is 11.14 am in the UK.

Bob

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

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

bobbym I can't help it but to admire you more.

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**295Ja****Member**- Registered: 2012-07-28
- Posts: 39

bob bundy thank you very much for being kind enough to explain further. I really appreciate it and I could say that I now understand it better.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Hi;

bobbym I can't help it but to admire you more.

If only someone I knew felt that way.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi bobbym,

Who do you count as " someone I knew" ?

Does it have to be past tense?

What I mean is: " I know you and I admire you more every day."

On the other hand, perhaps you were hoping for female admiration, in which case, I cannot help you there.

hi 295Ja

You are welcome.

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,248

Hi;

On the other hand, perhaps you were hoping for female admiration

A person like that could be described as a wolf or maybe just a darn fool.

What I mean is: " I know you and I admire you more every day."

That was my feeling about you so you can not borrow it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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