x/x^2 - 9 re-arranged as a quadratic equation

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acomber
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I have the equation:

y = \frac{x}{x^2 - 9}

I am asked to show how the equation can be rearranged as a quadratic equation in x provided y not equal 0

OK so I realise x/x^2 - 9 is a rational function. It could be expressed as:

\frac{x}{(x - 3)(x+3)}

So to express as an equation I could do like this:

\frac{x}{(x - 3)(x+3)} = 0

Is that a quadratic equation?

Is that all that is required?

Or do I have to do more? If so any hints would be much appreciated.
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TenOfThem
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(Original post by acomber)
I have the expression:

\frac{x}{x^2 - 9}

I am asked to show how the equation can be rearranged as a quadratic equation in x provided y not equal 0
THis make no sense

You cannot rearrange an expression to make an equation

There is no y in your question
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acomber
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Sorry I made a mistake - should be y = . I will edit question.
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TenOfThem
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(Original post by acomber)
Sorry I made a mistake - should be y = . I will edit question.
So now you have put y=0 in spite of the fact that the questions said y is not 0


The question still does not really make sense
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davros
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(Original post by acomber)
I have the equation:

y = \frac{x}{x^2 - 9}

I am asked to show how the equation can be rearranged as a quadratic equation in x provided y not equal 0

OK so I realise x/x^2 - 9 is a rational function. It could be expressed as:

\frac{x}{(x - 3)(x+3)}

So to express as an equation I could do like this:

\frac{x}{(x - 3)(x+3)} = 0

Is that a quadratic equation?


Is that all that is required?

Or do I have to do more? If so any hints would be much appreciated.
No idea why you're setting that equal to 0.

To rearrange your original equation as a quadratic equation in x, simply multiply both sides by the denominator then rearrange terms so it looks like a standard quadratic equation. There's no need to be factorizing anything at this stage.
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acomber
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I am confused still.

You mean like this:

y(x^2 - 9) = x

x^2y - 9y = x

Then what?

(Original post by davros)
No idea why you're setting that equal to 0.

To rearrange your original equation as a quadratic equation in x, simply multiply both sides by the denominator then rearrange terms so it looks like a standard quadratic equation. There's no need to be factorizing anything at this stage.
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Hasufel
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move the x over to the other side, so that it`s like:

ax^2+bx+c=0
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acomber
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You mean like this?

x^2y - 9y - x = 0


(Original post by Hasufel)
move the x over to the other side, so that it`s like:

ax^2+bx+c=0
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davros
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(Original post by acomber)
You mean like this?

x^2y - 9y - x = 0
Yes, although it would be more usual to write this as

yx^2 - x - 9y

to make it explicit that it is a quadratic equation in the variable x.
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