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

- anonymous

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

- schrodinger

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- anonymous

|dw:1315244053369:dw|

- anonymous

ok well ur gonna end up with this here hold on

- anonymous

20-(5x-25)=-5

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## More answers

- anonymous

so then (5x-25)=25

- anonymous

then 5x=50 and then x=10 :)

- anonymous

tht is very confusing to me, wht happened to the fractions?

- anonymous

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

- anonymous

|dw:1315244980380:dw|

- anonymous

I got (-5)/(5(x-5))

- anonymous

for the LHS or RHS?

- anonymous

mfleisch5's answer is incorrect btw.

- anonymous

oh ok

- anonymous

I trust you can take it from there?

- anonymous

I got (-5)/(5x-25)=(-5)/(5x-25)

- anonymous

how did you get -5/(5x-25) on the left hand side of the equation? can you show me the steps?

- anonymous

I multiplied the 5 and the x-5, then I thought the 4 was negative and added it with the 1

- anonymous

no, draw and show me. I don't understand what you just said.

- anonymous

first off all, 4 is not negative. secondly, that is not how you subtract fractions.

- anonymous

ok what about (-1)/(5(x-25)) = (-1)/(5(x-25))

- anonymous

|dw:1315245667613:dw|

- anonymous

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

- anonymous

|dw:1315245751739:dw|

- anonymous

no mfleisch5, x=10 is not the correct answer.

- anonymous

how is it not?

- anonymous

I got 15

- anonymous

\[\frac{4}{x-5} = \frac{4}{x-5} \times \frac{5}{5} = \frac{20}{5(x-5)}\]

- anonymous

similarly,
\[\frac{-1}{5} = \frac{-1}{5} \times \frac{x-5}{x-5} = \frac{-(x-5)}{5(x-5)}\]

- anonymous

exactly. and then u multiply the other one by x-5

- anonymous

so,
\[\frac{4}{x-5} - \frac{1}{5} = \frac{20}{5(x-5)} - \frac{x-5}{5(x-5)} = \frac{20-(x-5)}{5(x-5)}\]

- anonymous

no, because everything has 5(x-5) so u can take all of the denominators out

- anonymous

so the left hand side is
\[\frac{20-x+5}{5(x-5)} = \frac{25-x}{5(x-5)}\]

- anonymous

now, the right hand side is
\[\frac{-5}{5x-25} = \frac{-5}{5(x-5)}\]

- anonymous

that means
\[\frac{25-x}{5(x-5)} = \frac{-5}{5(x-5)}\]

- anonymous

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

- anonymous

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.

- anonymous

you get x = 30

- anonymous

got it, wolfgirl?
also, mfleisch5, you are still wrong. follow the steps I have shown.

- anonymous

almost, there are a lot of numbers

- anonymous

no. u are wrong. blah.

- anonymous

ignore mfleisch5, ignore the pictures I drew, just follow the steps I have shown

- anonymous

Let me know if you have any difficulties.

- anonymous

alright I got it thanks :)

- anonymous

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.

- anonymous

when you substitute x = 10 in
\[\frac{4}{x-5}-\frac{1}{5} = \frac{-5}{5x-25} \]
you get
\[\frac{4}{10-5}-\frac{1}{5} = \frac{-5}{50-25} \rightarrow \frac{4}{5}-\frac{1}{5} = \frac{-5}{25}\]
\[\frac{3}{5} = \frac{-1}{5}\]

- anonymous

which is a contradiction. therefore x = 10 is not the correct answer.

- anonymous

ok cool

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