Question

@e.mccormick another quick question, sorry

Answer 1

rearrange to find 2 solutions for x:

Answer 2

\[\frac{ 2 }{ x } + \frac{ 2 }{ x+1 } =3\]

Answer 3

OK. So you will need to get all the xes together and out of the denominator.

Answer 4

Lest start out the same as list time, common denominator, look for thigns that cancel.

Answer 5

x and x+1

Answer 6

(2x)+(2x+1)=3 ?

Answer 7

Lets see, which way did you work to get that? I was still writing some of it out.

Answer 8

haha ummm just distributed the tops, nah ignore me i've probs done it wrong. Just carry on

Answer 9

OK. I have an answer. So, distributing the tops is where we start. But you can't just ignore the bottom.

Answer 10

sorry yeah, so we have:

\[\frac{ 4x+1 }{ x*x+1 }\]
?

Answer 11

paren around the x+1 on the bottom, and it all still =3, other than that, yes.

Answer 12

Or... wait... +1 n the top? I have +2.

Answer 13

okay, what answer did you get?

Answer 14

Well, at that step I have: \[\frac{4x+2}{x({x+1)}}=3\] and the next sstep is to multiply out that \({x({x+1)\) so it is no longer in the denominator. That will put it on the right hand side.

Answer 15

Then it will be in a form where you can move over everything and have 0 on one side. That is the rearange to find solutions part.

Answer 16

so then 4x+2=3x*(x(x+1))

Answer 17

Yes. So if you subtract off the 4x+2 from both sides...

Answer 18

Then distribute, simplify, and you should be there.

Answer 19

\[0=3x \times x ^{2} +x\]

Answer 20

Somewhere you made a misstep. I see a 3x(x(x+1) there, which is an extra x. I think you just miswrote it when you carried it over. Distribute and simplify: \(0=3x(x+1)-(4x+2)\) See what you get then.

Answer 21

\[0=3x ^{2}+3x-4x+2\]
\[0=3x ^{2}-x+2\]
?

Answer 22

/cheer Yep. That is it. That is the form needed to find the answers to x, which is what they want,. The form, not the answers.

Answer 23

so then what would x be? do you have to use the quadratic formula?

Answer 24

Or if they want the actual solutions, then you would factor that and then you would solve each factor for x. But the way you wrote the question sems to make me thing they wanted the form. So... but if you need it all the way to x=, next would eb factoring that.

Answer 25

Well, quadratic works too.

Answer 26

-3.666667?

Answer 27

Looks like you have something a bit off. Rather than rushing right to the quadratic, why not try looking or afctors. Has anyone ever gone over that with you?

Answer 28

wait 0.6326...
and -0.96597...

Answer 29

See, when you multiply factors you get the polynmeal, this is doing it in reverse. Sometimes you can see them. It helps to do a lot of them so you se more of them.

Answer 30

I get 1 and -3/2. Want em to show you how I got there?

Answer 31

are they the right answers??

Answer 32

OK. So we have the \(3x^2-x-2\), right?

Answer 33

yup

Answer 34

Ah ha! I see, you misdistributed the - and had +2 above. That is messing up your quadratic.

Answer 35

That is the type of mistake that still kills me at times. I have made that same sort of error in uni.

Answer 36

oh so what are the actual answers?

Answer 37

1 and -3/2. If you look at the \(3x^2-x-2\) it has 3, 1, and 2 in it, which do not factor. So it must be two polyniomeals in the form of \((Ax\pm B)\) where the A and B are some combinations of 1, 1, 3, and 2.

Answer 38

okayy thanks, look i really need to go now

Answer 39

So I wrote out (3x+1)(x-2) as a first guess and used FOIL. I got the wrong result, but it was close. Next I did (3x+2)(x-1) and I foled that, and I got back what I wanted, so I knew it was right.

Answer 40

Not quite as quick as you wanted, but I hope it helps! Have fun with your time lapse stuff!