SOLUTION: Hello. I'm practicing for an exam and I need some help with the following problem. Solve the equation: x-3/x-2 - 1/x = x-3/x thanks!

Algebra ->  Equations -> SOLUTION: Hello. I'm practicing for an exam and I need some help with the following problem. Solve the equation: x-3/x-2 - 1/x = x-3/x thanks!      Log On


   

Question 189393: Hello. I'm practicing for an exam and I need some help with the following problem.
Solve the equation:
x-3/x-2 - 1/x = x-3/x
thanks!
Answer by greta_elisif(10) About Me  (Show Source):
You can put this solution on YOUR website!
x-3%2Fx-2+-+1%2Fx+=+x-3%2Fx
1. Subtract the quantity %28x-3%2Fx%29 from both sides
2. Then you have -+2+-+1%2Fx+=+0
3. Add 2 to both sides
4. Then you have -+1%2Fx+=+2
5. Multiply both sides by x
6. Then you have -+1+=+2x
7. Divide both sides by 2
8. Then you have -+1%2F2+=+x
But, it looks like you probably forgot some parentheses here.
So, I think your problem is actually:
%28x-3%29%2F%28x-2%29+-+1%2Fx+=+%28x-3%29%2Fx
1. Get common denominators by muliplying thusly:

2. You have
3. Subtract on the left side of the equation
4. Then you have: %28x%5E2+-+4x+%2B+2%29%2F%28x%5E2+-+2x%29+=+%28x%5E2+-+5x+%2B+6%29%2F%28x%5E2+-+2x%29
5. Multiply both sides by the quantity %28x%5E2+-+2x%29
6. Then you have x%5E2+-+4x+%2B+2+=+x%5E2+-+5x+%2B+6
7. Subtract x%5E2 from both sides
8. Then you have -+4x+%2B+2+=+-+5x+%2B+6
9. Subtract -+5x from both sides.
10. Then you have x+%2B+2+=+6
11. Subtract 2 from both sides.
12. Then you have x+=+4