anonymous
  • anonymous
I have started solving this problem but I got stuck at this part. 4x^3-6x^2-4x-5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Are we just simplifying?
anonymous
  • anonymous
No, solving
anonymous
  • anonymous
And checking for extraneous solutions.

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anonymous
  • anonymous
This is an expression, not an equation. It cannot be solved. If you will recheck your question, we can help you.
anonymous
  • anonymous
Yeah. If we're solving, there has to be an equal sign.
anonymous
  • anonymous
The original question was 10 over x squared +2x plus 4 over x= 5 over x-2
anonymous
  • anonymous
Is this the original question? \[\dfrac{10}{x^2+4}=\dfrac{5}{x-2}\]
anonymous
  • anonymous
You're missing the +2x after the x^2, @gypsy1274
anonymous
  • anonymous
No, 10/xsquared -2 plus 4/x
anonymous
  • anonymous
The last part is right
anonymous
  • anonymous
How's this? \[\dfrac{10}{x^2-2}+\dfrac{4}{x}=\dfrac{5}{x-2}\]
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Was you first step to find a common denominator? If so, what was it?
anonymous
  • anonymous
No, I multiplied each numerator by the opposite denominator on the left side
anonymous
  • anonymous
do you mean that you cross multiplied?
anonymous
  • anonymous
That is not possible since there are 2 terms on the left side.
anonymous
  • anonymous
Yes that's what I did
anonymous
  • anonymous
Here is what I did: Multiplied the entire equation by x. That will eliminate the fraction in the second term.
anonymous
  • anonymous
Then I multiplied the equation by x-2, to eliminate the fraction in the third term.
anonymous
  • anonymous
Now, I am looking at canceling....
anonymous
  • anonymous
Canceling isn't working. So I am multiplying by \(x^2-2\).
anonymous
  • anonymous
The factoring a third degree polynomial.
anonymous
  • anonymous
In am lost. I am stuck at 10+4/x-2=5/x
anonymous
  • anonymous
How did you get there?
anonymous
  • 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
  • anonymous
I got 10/x-2 plus 4=5/-2
anonymous
  • 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
  • anonymous
Yes
anonymous
  • anonymous
OK. Fix the rest of the equation, let me know what you get and we can move on from there.
anonymous
  • anonymous
Now I 10x/xsquared-2x+4=5/-2
anonymous
  • anonymous
Look again at your last term....I think something may be missing...
anonymous
  • anonymous
Oh, yeah. X-2
anonymous
  • anonymous
More than that.... \(\dfrac{5}{x-2} \times x=\)?
anonymous
  • anonymous
5x
anonymous
  • anonymous
\(\dfrac{5x}{x-2}\)
anonymous
  • anonymous
Now, multiply through by one of the remaining denominators. Show me your work for each term please.
anonymous
  • anonymous
Now I am at 10xsquared-2 over xsquared-2x plus 4x-8=5x
anonymous
  • anonymous
Which denominator did you multiply by?
anonymous
  • anonymous
X-2
anonymous
  • anonymous
Stupid moment, don't mind me.
anonymous
  • anonymous
3rd
anonymous
  • anonymous
Remember to distribute....The 10x needs to multiply by each term.
anonymous
  • anonymous
Don't get it
anonymous
  • 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
  • anonymous
Okay, so then it's 20x-2x?
anonymous
  • anonymous
Not quite... \(10x \times x=\)?
anonymous
  • anonymous
20xsquared-2x?
anonymous
  • anonymous
No, try again.
anonymous
  • anonymous
Start with \(10x \times x=\)
anonymous
  • anonymous
10xsquared
anonymous
  • anonymous
??
anonymous
  • anonymous
Yes. and \(-2 \times x = \)?
anonymous
  • anonymous
10x^2 and -2x
anonymous
  • anonymous
OK. It's getting to be time for me to sign off. \(10x(x-2) = 10x^2 -20x\)
anonymous
  • 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
  • anonymous
Okay, thankyou so much

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