SOLUTION: How to simplify the following algebraic expression: (a) (x / x -2)/ (x +1/ x -2)

Question 847191: How to simplify the following algebraic expression:
(a) (x / x -2)/ (x +1/ x -2)

Found 2 solutions by swincher4391, dg181625:
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Just like you learned with normal fractions. Keep, Change, Flip.
Keep x/(x-2)
Change division to multiplication
Flip (x+1)/(x-2) as (x-2)/(x+1)

Now the resulting multiplication has (x-2) cancelling out giving us just x/(x+1)
Answer by dg181625(2) (Show Source): You can put this solution on YOUR website!
(x / x -2) / (x +1/ x -2)
A fraction is divided by a fraction. So just multiply the reciprocal; which is flipping the second fraction.
( x / x -2) (x -2 / x +1) =

Since (x-2) is on the numerator of one side and the denominator of the other, they cancelled each other out.
So the Answer is just: ( x / x+1 )

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