## anonymous 4 years ago (4)/(x-5)-(1)/(5) = (-5)/(5x-25)

1. anonymous

|dw:1315244053369:dw|

2. anonymous

ok well ur gonna end up with this here hold on

3. anonymous

20-(5x-25)=-5

4. anonymous

so then (5x-25)=25

5. anonymous

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

6. anonymous

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

7. 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

8. anonymous

|dw:1315244980380:dw|

9. anonymous

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

10. anonymous

for the LHS or RHS?

11. anonymous

12. anonymous

oh ok

13. anonymous

I trust you can take it from there?

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

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

18. anonymous

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

19. anonymous

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

20. anonymous

|dw:1315245667613:dw|

21. 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

22. anonymous

|dw:1315245751739:dw|

23. anonymous

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

24. anonymous

how is it not?

25. anonymous

I got 15

26. anonymous

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

27. anonymous

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

28. anonymous

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

29. anonymous

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

30. anonymous

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

31. anonymous

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

32. anonymous

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

33. anonymous

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

34. 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

35. 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.

36. anonymous

you get x = 30

37. anonymous

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

38. anonymous

almost, there are a lot of numbers

39. anonymous

no. u are wrong. blah.

40. anonymous

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

41. anonymous

Let me know if you have any difficulties.

42. anonymous

alright I got it thanks :)

43. 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.

44. anonymous

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

45. anonymous

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

46. anonymous

ok cool

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