SOLUTION: Hello tutor- this is an algebraic equation involving fractions. I know I have to find the LCD- but I am a bit lost...Thanks. Show the steps that you would take to solve the foll

Algebra ->  Systems-of-equations -> SOLUTION: Hello tutor- this is an algebraic equation involving fractions. I know I have to find the LCD- but I am a bit lost...Thanks. Show the steps that you would take to solve the foll      Log On


   

Question 190451: Hello tutor- this is an algebraic equation involving fractions. I know I have to find the LCD- but I am a bit lost...Thanks.
Show the steps that you would take to solve the following algebraically:
(3)/(x-3)=(x)/(x-3)-(3)/(2)

What potential solution did you obtain? Explain why this is not a solution.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%28x-3%29=x%2F%28x-3%29-3%2F2 Start with the given equation


Multiply EVERY term by the LCD 2%28x-3%29


2%283%29=2%28x%29-3%28x-3%29 Simplify


6=2x-3x%2B9 Distribute and multiply


6=-x%2B9 Combine like terms.


6-9=-x Subtract 9 from both sides


-3=-x Combine like terms.


3=x Divide both sides by -1 to isolate "x"


x=3 Rearrange the terms.


So a possible solution is x=3, but we need to check it. So plug it back into the original equation


3%2F%28x-3%29=x%2F%28x-3%29-3%2F2 Start with the given equation


3%2F%283-3%29=3%2F%283-3%29-3%2F2 Plug in x=3


3%2F0=3%2F0-3%2F2 Combine like terms.


Since division by zero is undefined, this means that x=3 is NOT a solution (since it isn't even in the domain).


So there are no solutions.