Question

Even more math review!

8b. Solve the equation. (Find only the real solutions)

Answer 1

Posting equation in a few seconds...

Answer 2

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

Answer 3

any idea how to start ?

Answer 4

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

Answer 5

x=1

Answer 6

@dinamix no direct answers please. Thank you

Answer 7

ok, sorry

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

yep the denominators are definitely not the same

Answer 13

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

Answer 14

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

Answer 15

now you can equate to zero and solve for x

Answer 16

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

Answer 17

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

Answer 18

*?

Answer 19

yes

Answer 20

you can substitute x for 1 to check ur answer

Answer 21

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?

Answer 22

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

Answer 23

x= 1 its easy why thiss???

Answer 24

@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 ;-;

Answer 25

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

Answer 26

it sure does. thanks, both of you

Answer 27

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"

Answer 28

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.

Answer 29

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

Answer 30

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.

Answer 31

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

Answer 32

sorry anway