Question

1200/x- 40 - 1200/x = 20/60

Answer 1

\[\frac{ 1200 }{ x - 40 } - \frac{ 1200 }{ x } = \frac{ 20 }{ 60 }\]

Answer 2

@rvc

Answer 3

@zepdrix

Answer 4

multiply every term by \(60x(x-40)\)

\[60x(x-40)(\frac{ 1200 }{ x - 40 }) - 60x(x-40)(\frac{ 1200 }{ x }) = 60x(x-40)(\frac{ 20 }{ 60 })\]

\[60x\cancel{(x-40)}(\frac{ 1200 }{ \cancel{x - 40} }) - 60\cancel{x}(x-40)(\frac{ 1200 }{ \cancel{x} }) = \cancel{60}x(x-40)(\frac{ 20 }{ \cancel{60} })\]

\[60x(1200)-60(x-40)1200=x(x-40)(20)\]

Answer 5

can you get it from here?

Answer 6

#justgotlost :(

Answer 7

I am going to need more than that to help you

Answer 8

???

Answer 9

I typed a bunch of stuff and your response is a hashtag, which tells me exactly nothing about where you are confused. If you clarify then I might be able to help

Answer 10

Look,I'm doing this chapter/topic after MONTHS , so I have no idea as to what to do.
And
Why did you take
The LCM
as
60x(x-40)?

Answer 11

Because that is what it is.

Answer 12

you dont have to find the least, but it will save you time often. you can ALWAYS just take the product of the denominators. i.e. given \[\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\]

Then we have

\[abc\frac{1}{a}+abc\frac{1}{b}=abc\frac{1}{c}\]

\[bc+ac=ab\]

Answer 13

make sense?

Answer 14

Yes.

Answer 15

If you have any questions, ask Galois (@rational). I got to sleep. Good luck

Answer 16

@rational
@Michele_Laino

Answer 17

I'll write the same equation as
\[\frac{ 1200 }{ x } - \frac{ 1200 }{ x - 40 } = \frac{ 1 }{ 3 }\]
Can't I?

Answer 18

yes you can!

Answer 19

So then
\[84,000 = x^2 + 40x ?!?!?!\]

Answer 20

there is an error of sign, since your equation is:
\[\frac{{1200}}{{x - 40}} - \frac{{1200}}{x} = \frac{1}{3}\]

Answer 21

now, the least common multiple is:
3x(x-40), so your equation is equivalent to this one:
\[1200 \cdot 3x - 1200 \cdot 3\left( {x - 40} \right) = x\left( {x - 40} \right)\]

Answer 22

x^2 + 40x - 84,000 = 0?

Answer 23

no, we have:
\[{x^2} - 40x - 144000 = 0\]

Answer 24

How??

Answer 25

3*1200*40= 144000

Answer 26

Oh I got my mistake.
What next how do I even factor this!?!

Answer 27

you have to solve that equation above, using this formula:
\[x = \frac{{40 \pm \sqrt {{{40}^2} + 4 \times 144000} }}{2} = ...?\]

Answer 28

what do you get?

Answer 29

I'm suppose to factor it and not use the formula -_-

Answer 30

it is the sam, since if you want to factor a polynomial, in general,, you have to find the roots of that polynomial

Answer 31

same*

Answer 32

hint:
\[\Large \sqrt {{{40}^2} + 4 \times 144000} = 760\]

Answer 33

"I'm suppose to factor it and not use the formula -_-"

Answer 34

I understand, nevertheless, in order to factorize your polynomial, you have to compute the roots of your polynomial, first

Answer 35

What?

Answer 36

performing the computation which I wrote above, namely:
\[x = \frac{{40 \pm \sqrt {{{40}^2} + 4 \times 144000} }}{2} = \frac{{40 \pm 760}}{2} = ...?\]

Answer 37

you should get two values

Answer 38

Can we factor it please?pleeeeeeeeeeeeease?

Answer 39

\[\begin{gathered}
{x_1} = \frac{{40 + 760}}{2} = ...? \hfill \\
\hfill \\
{x_2} = \frac{{40 - 760}}{2} = ...? \hfill \\
\end{gathered} \]

Answer 40

please, we need to know those two values above, in order to make the factorization

Answer 41

here is your factorization:
\[{x^2} - 40x - 144000 = \left( {x - {x_1}} \right)\left( {x - {x_2}} \right)\]

Answer 42

400
-360

Answer 43

perfect! So your factorization is:
\[{x^2} - 40x - 144000 = \left( {x + 360} \right)\left( {x - 400} \right)\]

Answer 44

????????????????????????????????????????????????????????????????????????????????????????
I thought it would be - 360 and +400
Whats wrong
????????????????????????????????????????????????????????????????????????????????????????

Answer 45

you have to replace x_1 with -360, and x_2 with 400 into this formula:
\[{x^2} - 40x - 144000 = \left( {x - {x_1}} \right)\left( {x - {x_2}} \right)\]
what do you get?

Answer 46

idk :(

Answer 47

here is more steps:
\[\begin{gathered}
\left( {x - {x_1}} \right)\left( {x - {x_2}} \right) = \left\{ {x - \left( { - 360} \right)} \right\}\left( {x - 400} \right) = \hfill \\
\hfill \\
= \left( {x + 360} \right)\left( {x - 400} \right) \hfill \\
\end{gathered} \]

Answer 48

here are*

Answer 49

so v r look at 400 then?