Even more math review!
8b. Solve the equation. (Find only the real solutions)

- Jamierox4ev3r

Even more math review!
8b. Solve the equation. (Find only the real solutions)

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- chestercat

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- Jamierox4ev3r

Posting equation in a few seconds...

- Jamierox4ev3r

\(\huge\frac{2x}{x+1} = \huge\frac{2x-1}{x}\)

- Nnesha

any idea how to start ?

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## More answers

- Jamierox4ev3r

hmm... let's see. I assume you would multiply both sides by the conjugate?

- dinamix

x=1

- Jamierox4ev3r

@dinamix no direct answers please. Thank you

- dinamix

ok, sorry

- Nnesha

hmm `cross multiply` \[\huge\rm \frac{ a }{ b}=\frac{ c }{ d } \]\[\huge\rm ad =bc\]

- nincompoop

what happens when you do that, Jamie?
There are maybe different way to approach, but let us see what will happen

- nincompoop

but if we made it our goal so that we do not have to deal with denominators since they do not look the same, then cross multiplication would be an easier route

- Jamierox4ev3r

oh right. Cross multiplying is a thing. And I tried multiplying by a conjugate, but that actually seems to get kind of messy.

- Jamierox4ev3r

yep the denominators are definitely not the same

- Nnesha

when you see `equal` sign between two fractions
then u should `cross multiply`

- Jamierox4ev3r

If you cross multiply, it seems as if you get \(2x^{2} = 2x^{2}+x-1\)
And thank you @Nnesha , seems like a good rule of thumb

- nincompoop

now you can equate to zero and solve for x

- nincompoop

I do not understand cross-multiplication. It is not a true mathematical procedure.

- Jamierox4ev3r

o-o in that case, wouldn't x be 1.

- Jamierox4ev3r

*?

- Nnesha

yes

- Nnesha

you can substitute x for 1 to check ur answer

- Jamierox4ev3r

a'ight then. When substituted, things look kosher (equivalent) so looks like I'm fine. But question. @nincompoop how do you know that you can squat \(2x^{2}\) to zero?

- nincompoop

the equation will be set to zero by moving all of your expressions on one side and zero on the other side

- dinamix

x= 1 its easy why thiss???

- Jamierox4ev3r

@dinamix I know it seems simple to just give an answer. Sadly, this does not help the user learn. So I prefer a process to be explained so I will have a strong understanding of how to do problems that are similar in the future
and @nincompoop thank you ;-;

- nincompoop

cross multiplication is not a true mathematical procedure tho, but it helps

- Jamierox4ev3r

it sure does. thanks, both of you

- nincompoop

in cross-multiplication, we skip fundamental algebraic steps because they are supposedly understood for someone who is been doing it over and over. I can show you ALL the steps which lead to the idea of "cross-multiplication"

- Jamierox4ev3r

If you have the time to explain, feel free. I never did understand the true mathematical processes behind cross multiplication. In my freshman algebra days, we were simply told to do it because it would give us right answers.

- nincompoop

it is a good way to do the review since you are about to do calculus soon, which require rigorous algebraic acrobat knowledge.

- Jamierox4ev3r

indeed. and I am quite aware. I've decided to focus on algebra the most for my review, since trig, conics, and other pre-calculus things are still fresh in my mind.

- dinamix

@Jamierox4ev3rok , @nincompoop forgive me i f i was rude

- dinamix

sorry anway

- nincompoop

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- Jamierox4ev3r

I'll be back later, I have a class that I should probably get going to in a bit. Thank you so much in advance though @nincompoop

- nincompoop

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