SOLUTION: verify that (2x+1)/x-1 is the inverse of x+1/x-2 . I only got to x= y+1/y-2 and got stuck on how to simplify.

Question 56862This question is from textbook
: verify that (2x+1)/x-1 is the inverse of x+1/x-2 . I only got to x= y+1/y-2 and got stuck on how to simplify. This question is from textbook

Answer by Scriptor(36) (Show Source): You can put this solution on YOUR website!
Suppose f(x) = (2x+1)/(x-1) and g(x)= x+1/x-2
Now you have to check that f(g(x))= x
Let's check this:
f(g(x)) = (2*g(x)+1)/(g(x)-1)

= [2*(x+1/x-2) + 1]/(x+1/x-2 -1)
= [2*(x+1/x-2)+(x-2/x-2]/[x+1/x-2)-(x-2/x-2)]

= [(2x+2+x-2)/(x-2)] / [x+1-x+2/(x-2)]

= 2x+2+x-x / x+1-x+2

= x
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