SOLUTION: A). Show the steps that you would take to solve the following algebraically: 3/x-3 = x/x-3 minus 3/2 B.) What potential solution did you obtain. Explain why this is not

Algebra ->  Square-cubic-other-roots -> SOLUTION: A). Show the steps that you would take to solve the following algebraically: 3/x-3 = x/x-3 minus 3/2 B.) What potential solution did you obtain. Explain why this is not       Log On


   

Question 151530: A).
Show the steps that you would take to solve the following algebraically:

3/x-3 = x/x-3 minus 3/2

B.) 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!
A)


%283%29%2F%28x-3%29=%28x%29%2F%28x-3%29-%283%29%2F%282%29 Start with the given equation.


Multiply every term on both sides by the LCD 2%28x-3%29. Doing this will eliminate all of the fractions.



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


2%283%29=2%28x%29-3%28x-3%29 Rearrange the terms


2%283%29=2%28x%29-3x%2B9 Distribute


6=2x-3x-9 Multiply


6-9=2x-3x Subtract 9 from both sides.


-3=-x Combine like terms.


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


So the possible solution is x=3


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B)


Let's see why this possible solution is not a real solution


%283%29%2F%28x-3%29=%28x%29%2F%28x-3%29-%283%29%2F%282%29 Start with the given equation.


%283%29%2F%283-3%29=%283%29%2F%283-3%29-%283%29%2F%282%29 Plug in x=3


%283%29%2F%280%29=%283%29%2F%280%29-%283%29%2F%282%29 Subtract


Since division by zero is not possible, this means that x=3 is not a real solution.


So this means that there are no real solutions.