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(4)/(x-5)-(1)/(5) = (-5)/(5x-25)

Mathematics
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|dw:1315244053369:dw|
ok well ur gonna end up with this here hold on
20-(5x-25)=-5

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Other answers:

so then (5x-25)=25
then 5x=50 and then x=10 :)
tht is very confusing to me, wht happened to the fractions?
first step: subtract 1/5 from 4/x-5 and post what you get. you know how to subtract fractions I assume? take LCM and cross multiply to subtract the LHS expression
|dw:1315244980380:dw|
I got (-5)/(5(x-5))
for the LHS or RHS?
mfleisch5's answer is incorrect btw.
oh ok
I trust you can take it from there?
I got (-5)/(5x-25)=(-5)/(5x-25)
how did you get -5/(5x-25) on the left hand side of the equation? can you show me the steps?
I multiplied the 5 and the x-5, then I thought the 4 was negative and added it with the 1
no, draw and show me. I don't understand what you just said.
first off all, 4 is not negative. secondly, that is not how you subtract fractions.
ok what about (-1)/(5(x-25)) = (-1)/(5(x-25))
|dw:1315245667613:dw|
wolfgirl, all you have to do is multiply 5 and x-5. once u do that, you will have all common denominators, so you can cross them out. then you are left with what i gave you, and the answer is x=10
|dw:1315245751739:dw|
no mfleisch5, x=10 is not the correct answer.
how is it not?
I got 15
\[\frac{4}{x-5} = \frac{4}{x-5} \times \frac{5}{5} = \frac{20}{5(x-5)}\]
similarly, \[\frac{-1}{5} = \frac{-1}{5} \times \frac{x-5}{x-5} = \frac{-(x-5)}{5(x-5)}\]
exactly. and then u multiply the other one by x-5
so, \[\frac{4}{x-5} - \frac{1}{5} = \frac{20}{5(x-5)} - \frac{x-5}{5(x-5)} = \frac{20-(x-5)}{5(x-5)}\]
no, because everything has 5(x-5) so u can take all of the denominators out
so the left hand side is \[\frac{20-x+5}{5(x-5)} = \frac{25-x}{5(x-5)}\]
now, the right hand side is \[\frac{-5}{5x-25} = \frac{-5}{5(x-5)}\]
that means \[\frac{25-x}{5(x-5)} = \frac{-5}{5(x-5)}\]
if that is true then that would mean there would be unlimited answers because no matter what u put for x it will work out. u are wrong hatra! its 10
the denominators are the same on both sides of the equation. that means the numerators are equal too. so, \[25-x = -5\] solve for x.
you get x = 30
got it, wolfgirl? also, mfleisch5, you are still wrong. follow the steps I have shown.
almost, there are a lot of numbers
no. u are wrong. blah.
ignore mfleisch5, ignore the pictures I drew, just follow the steps I have shown
Let me know if you have any difficulties.
alright I got it thanks :)
also, mfleisch5, substitute 10 in the original equation and see if it is right. its a very easy test to see if your answer is correct or not.
when you substitute x = 10 in \[\frac{4}{x-5}-\frac{1}{5} = \frac{-5}{5x-25} \] you get \[\frac{4}{10-5}-\frac{1}{5} = \frac{-5}{50-25} \rightarrow \frac{4}{5}-\frac{1}{5} = \frac{-5}{25}\] \[\frac{3}{5} = \frac{-1}{5}\]
which is a contradiction. therefore x = 10 is not the correct answer.
ok cool

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