Questions on Algebra: Square root, cubic root, N-th root answered by real tutors!

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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. : 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(9217) About Me  (Show Source):
You can put this solution on YOUR website!
A)


(3)/(x-3)=(x)/(x-3)-(3)/(2) Start with the given equation.


2cross((x-3))((3)/cross((x-3)))=2cross((x-3))((x)/cross(x-3))-cross(2)(x-3)((3)/cross(2)) Multiply every term on both sides by the LCD 2(x-3). Doing this will eliminate all of the fractions.



2(3)=2(x)-(x-3)(3) Simplify


2(3)=2(x)-3(x-3) Rearrange the terms


2(3)=2(x)-3x+9 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


(3)/(x-3)=(x)/(x-3)-(3)/(2) Start with the given equation.


(3)/(3-3)=(3)/(3-3)-(3)/(2) Plug in x=3


(3)/(0)=(3)/(0)-(3)/(2) 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.