Question

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

Answer 1

Are we just simplifying?

Answer 2

No, solving

Answer 3

And checking for extraneous solutions.

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

No, 10/xsquared -2 plus 4/x

Answer 10

The last part is right

Answer 11

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

Answer 12

Yes

Answer 13

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

Answer 14

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

Answer 15

do you mean that you cross multiplied?

Answer 16

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

Answer 17

Yes that's what I did

Answer 18

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

Answer 19

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

Answer 20

Now, I am looking at canceling....

Answer 21

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

Answer 22

The factoring a third degree polynomial.

Answer 23

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

Answer 24

How did you get there?

Answer 25

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?

Answer 26

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

Answer 27

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?

Answer 28

Yes

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

Oh, yeah. X-2

Answer 33

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

Answer 34

5x

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

Which denominator did you multiply by?

Answer 39

X-2

Answer 40

Stupid moment, don't mind me.

Answer 41

3rd

Answer 42

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

Answer 43

Don't get it

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

20xsquared-2x?

Answer 48

No, try again.

Answer 49

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

Answer 50

10xsquared

Answer 51

??

Answer 52

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

Answer 53

10x^2 and -2x

Answer 54

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

Answer 55

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.

Answer 56

Okay, thankyou so much