wolfgirl
(4)/(x-5)-(1)/(5) = (-5)/(5x-25)
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wolfgirl
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mfleisch5
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ok well ur gonna end up with this here hold on
mfleisch5
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20-(5x-25)=-5
mfleisch5
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so then (5x-25)=25
mfleisch5
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then 5x=50 and then x=10 :)
wolfgirl
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tht is very confusing to me, wht happened to the fractions?
dhatraditya
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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
dhatraditya
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|dw:1315244980380:dw|
wolfgirl
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I got (-5)/(5(x-5))
dhatraditya
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for the LHS or RHS?
dhatraditya
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mfleisch5's answer is incorrect btw.
wolfgirl
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oh ok
dhatraditya
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I trust you can take it from there?
wolfgirl
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I got (-5)/(5x-25)=(-5)/(5x-25)
dhatraditya
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how did you get -5/(5x-25) on the left hand side of the equation? can you show me the steps?
wolfgirl
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I multiplied the 5 and the x-5, then I thought the 4 was negative and added it with the 1
dhatraditya
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no, draw and show me. I don't understand what you just said.
dhatraditya
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first off all, 4 is not negative. secondly, that is not how you subtract fractions.
wolfgirl
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ok what about (-1)/(5(x-25)) = (-1)/(5(x-25))
dhatraditya
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mfleisch5
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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
dhatraditya
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dhatraditya
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no mfleisch5, x=10 is not the correct answer.
mfleisch5
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how is it not?
wolfgirl
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I got 15
dhatraditya
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\[\frac{4}{x-5} = \frac{4}{x-5} \times \frac{5}{5} = \frac{20}{5(x-5)}\]
dhatraditya
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similarly,
\[\frac{-1}{5} = \frac{-1}{5} \times \frac{x-5}{x-5} = \frac{-(x-5)}{5(x-5)}\]
mfleisch5
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exactly. and then u multiply the other one by x-5
dhatraditya
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so,
\[\frac{4}{x-5} - \frac{1}{5} = \frac{20}{5(x-5)} - \frac{x-5}{5(x-5)} = \frac{20-(x-5)}{5(x-5)}\]
mfleisch5
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no, because everything has 5(x-5) so u can take all of the denominators out
dhatraditya
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so the left hand side is
\[\frac{20-x+5}{5(x-5)} = \frac{25-x}{5(x-5)}\]
dhatraditya
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now, the right hand side is
\[\frac{-5}{5x-25} = \frac{-5}{5(x-5)}\]
dhatraditya
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that means
\[\frac{25-x}{5(x-5)} = \frac{-5}{5(x-5)}\]
mfleisch5
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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
dhatraditya
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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.
dhatraditya
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you get x = 30
dhatraditya
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got it, wolfgirl?
also, mfleisch5, you are still wrong. follow the steps I have shown.
wolfgirl
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almost, there are a lot of numbers
mfleisch5
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no. u are wrong. blah.
dhatraditya
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ignore mfleisch5, ignore the pictures I drew, just follow the steps I have shown
dhatraditya
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Let me know if you have any difficulties.
wolfgirl
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alright I got it thanks :)
dhatraditya
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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.
dhatraditya
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when you substitute x = 10 in
\[\frac{4}{x-5}-\frac{1}{5} = \frac{-5}{5x-25} \]
you get
\[\frac{4}{10-5}-\frac{1}{5} = \frac{-5}{50-25} \rightarrow \frac{4}{5}-\frac{1}{5} = \frac{-5}{25}\]
\[\frac{3}{5} = \frac{-1}{5}\]
dhatraditya
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which is a contradiction. therefore x = 10 is not the correct answer.
wolfgirl
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ok cool