I have started solving this problem but I got stuck at this part. 4x^3-6x^2-4x-5

- anonymous

I have started solving this problem but I got stuck at this part. 4x^3-6x^2-4x-5

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- anonymous

Are we just simplifying?

- anonymous

No, solving

- anonymous

And checking for extraneous solutions.

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## More answers

- anonymous

This is an expression, not an equation. It cannot be solved. If you will recheck your question, we can help you.

- anonymous

Yeah. If we're solving, there has to be an equal sign.

- anonymous

The original question was 10 over x squared +2x plus 4 over x= 5 over x-2

- anonymous

Is this the original question?
\[\dfrac{10}{x^2+4}=\dfrac{5}{x-2}\]

- anonymous

You're missing the +2x after the x^2, @gypsy1274

- anonymous

No, 10/xsquared -2 plus 4/x

- anonymous

The last part is right

- anonymous

How's this?
\[\dfrac{10}{x^2-2}+\dfrac{4}{x}=\dfrac{5}{x-2}\]

- anonymous

Yes

- anonymous

Was you first step to find a common denominator? If so, what was it?

- anonymous

No, I multiplied each numerator by the opposite denominator on the left side

- anonymous

do you mean that you cross multiplied?

- anonymous

That is not possible since there are 2 terms on the left side.

- anonymous

Yes that's what I did

- anonymous

Here is what I did:
Multiplied the entire equation by x.
That will eliminate the fraction in the second term.

- anonymous

Then I multiplied the equation by x-2, to eliminate the fraction in the third term.

- anonymous

Now, I am looking at canceling....

- anonymous

Canceling isn't working. So I am multiplying by \(x^2-2\).

- anonymous

The factoring a third degree polynomial.

- anonymous

In am lost. I am stuck at 10+4/x-2=5/x

- anonymous

How did you get there?

- anonymous

If you were following my steps, lets go through them one at a time.
What did you get after multiplying the entire equation by x?

- anonymous

I got 10/x-2 plus 4=5/-2

- anonymous

You cannot cancel out part of a term, It is an all or nothing deal. So...
\[\dfrac{10}{x^2-2} \times x = \dfrac{10x}{x^2-2}\]
Does that make sense?

- anonymous

Yes

- anonymous

OK. Fix the rest of the equation, let me know what you get and we can move on from there.

- anonymous

Now I 10x/xsquared-2x+4=5/-2

- anonymous

Look again at your last term....I think something may be missing...

- anonymous

Oh, yeah. X-2

- anonymous

More than that....
\(\dfrac{5}{x-2} \times x=\)?

- anonymous

5x

- anonymous

\(\dfrac{5x}{x-2}\)

- anonymous

Now, multiply through by one of the remaining denominators. Show me your work for each term please.

- anonymous

Now I am at 10xsquared-2 over xsquared-2x plus 4x-8=5x

- anonymous

Which denominator did you multiply by?

- anonymous

X-2

- anonymous

Stupid moment, don't mind me.

- anonymous

3rd

- anonymous

Remember to distribute....The 10x needs to multiply by each term.

- anonymous

Don't get it

- anonymous

You multiplied the equation by x-2. The numerator of the first term is 10x so you need to multiply 10x(x-2). \((10x \times x)+ (10x \times -2)\)

- anonymous

Okay, so then it's 20x-2x?

- anonymous

Not quite...
\(10x \times x=\)?

- anonymous

20xsquared-2x?

- anonymous

No, try again.

- anonymous

Start with \(10x \times x=\)

- anonymous

10xsquared

- anonymous

??

- anonymous

Yes. and \(-2 \times x = \)?

- anonymous

10x^2 and -2x

- anonymous

OK. It's getting to be time for me to sign off.
\(10x(x-2) = 10x^2 -20x\)

- anonymous

Put it all together and you get:
\[x^3+2x^2-18x+16=0\]
Hopefully you will get the same thing when you combine like terms. Unfortunately, at this point, I have to abandon you because I don't know how to factor a third degree polynomial.
I suggest you close this question and ask a new one. Just cut and paste from below.
`\[x^3+2x^2-18x+16=0\]`
And ask someone how to factor it.

- anonymous

Okay, thankyou so much

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