SOLUTION: Okay, I worked this one out twice and am still not sure about it. x/x-2 -5/1 = 2/x-2 This is what I did: x/x-2 -5/1 = 2/x-2 I find the common denominator which is x-2. I mu

Question 18152: Okay, I worked this one out twice and am still not sure about it.
x/x-2 -5/1 = 2/x-2
This is what I did:
x/x-2 -5/1 = 2/x-2 I find the common denominator which is x-2. I multiply with x-2.
That gives me x-(5x-10)/x-2 = 2/x-2
so now I have 4x + 10 = 2, I subtract -10 from both sides which gives me 4x = -8 divide both sides by 4
that gives me x= -2
Did I do this right???
Thanks for any and all responses.
lizzy

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Okay, I worked this one out twice and am still not sure about it.
x/x-2 -5/1 = 2/x-2
This is what I did:
SEE MY COMMENTS POSTED IN CAPITAL LETTERS....
x/x-2 -5/1 = 2/x-2 I find the common denominator which is x-2. I multiply with x-2.**********OK.BUT PROPER WAY IS TO SAY THAT YOU ARE MULTIPLYING THROUGHOUT WITH (x-2)AND DO THAT WAY..ONE CAUTION HERE YOU ARE NOT ALLOWED IN MATHS TO MULTIPLY OR DIVIDE ALL TERMS OF AN EQUATION WITH ZERO.WHEN AN UNKNOWN IS INVOLVED WHICH MAY BE ZERO WE BETTER MENTION IT AS A GOOD PRACTICE.HERE WE ARE MULTIPLYING WITH x-2 AN UNKNOWN WHICH COULD BE ZERO IF x=2.SO WE SHOULD MENTION THAT ASSUMING x.IS NOT EQUAL TO 2......OR GOING BY YOUR WAY...LET US PROCEED
That gives me x-(5x-10)/x-2 = 2/x-2..OK
so now I have 4x + 10 = 2, I subtract -10 from both sides which gives me 4x = -8 divide both sides by 4...HERE YOU MADE A MISTAKE YOU GET -4x+10=2 NOT 4x+10=2
that gives me x= -2...NO..YOU GET x=2...NOW HERE IS THE CATCH YOU SEE WE GOT x=2 WHICH MAKES OUR FIRST OPERATION OF MULTIPLYING WITH x-2 ILLEGAL..SO WE WILL END UP WITH AN IMPOSSIBILITY AND x=2 CANOT BE THE ANSWER.THAT IS IF YOU TRY TO VERIFY THE ANSWER BY SUBSTITUTING WITH x=2 (INCIDENTALLY TILL YOU GAIN EXPERIENCE YOU DO VERIFICATION OF ALL THE PROBLEMS BY CHECKING YOUR ANSWER.YOU WOULD HAVE KNOWN THAT x=-2 YOU GOT IS NOT CORRECT IN THAT WAY )YOU WILL NOT GET IT RIGHT AS WE CAN SEE
x/x-2 -5/1 = 2/x-2 WILL GIVE US DIVISION BY ZERO ..
INFACT THE ROOT CAUSE FOR ALL THIS IS YOUR PROBLEM WHICH IF WE ANALYSE COMES TO THAT 1=5 ?????AS YOU CAN SEE BELOW
x/x-2 -5/1 = 2/x-2 ...or
(x/x-2)-(2/x-2)=5/1..or
(x-2)/(x-2)=5...or
1=5?????IF DIVISION BY x-2 IS PERMITTED...SO THAT IS IT....YOU DID WELL AND ALMOST GOT IT RIGHT .KEEP IT UP CORRECTING YOUR SLIPS...YOU WILL SUCCEED...IF YOU NEED FURTHER ELABORATION COME BACK
Did I do this right???
Thanks for any and all responses.
lizzy

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