SOLUTION: can someone please help and show me how to solve the following algebraically: 3/x-3=x/x-3-3/2

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Question 150798This question is from textbook
: can someone please help and show me how to solve the following algebraically:
3/x-3=x/x-3-3/2 This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
3%2F%28x-3%29+=+x%2F%28x-3%29-3%2F2 Did I get this right? It helps a lot if you use parentheses, thus:
3/(3-x) = x/(3-x) - 3/2
Anyway, let's proceed.
3%2F%28x-3%29+=+x%2F%28x-3%29+-+3%2F2 Subtract the fractions on the right using 2(x-3) as the LCD
3%2F%28x-3%29+=+%282x-3%28x-3%29%29%2F2%28x-3%29 Simplify the right numerator.
3%2F%28x-3%29+=+%282x-3x%2B9%29%2F2%28x-3%29
3%2F%28x-3%29+=+%28-x%2B9%29%2F2%28x-3%29 Now multiply both sides by 2.
6%2F%28x-3%29+=+%28-x%2B9%29%2F%28x-3%29 so...
6+=+-x%2B9
x+=+3
However, when you try to check this solution, you'll find that you have undefined quantities:
3%2F%28x-3%29+=+x%2F%28x-3%29-3%2F2 Substitute x = 3.
3%2F%283-3%29+=+3%2F%283-3%29-3%2F2
highlight%283%2F0%29+=+highlight%283%2F0%29-3%2F2 Division by zero is not defined in mathematics!
So, the solution is UNDEFINED.