Find the inverse of F(x)=x+1/x-2?

y = F(x) = (x + 1)/(x - 2)
y = (x + 1)/(x - 2)
y(x - 2) = x + 1
xy - 2y = x + 1
xy - x = 2y + 1
x(y - 1) = 2y + 1
x = (2y + 1)/(y - 1)

F⁻¹(x) = (2x + 1)/(x - 1)

I'll invert my foot in your @$$ if you ever speak to me like that again

Trump's tax returns..

y = (x+1)/(x-2)

Switch x and y
x = (y+1)/(y-2)
solve for y

multiply both sides by y-2
x(y-2) = y+1
xy-2x = y+1
xy-y = 2x+1
y(x-1) = 2x+1
divide both sides by x-1
y = (2x+1)/(x-1)

f^-1(x) = (2x+1)/(x-1)

Will assume that should be shown with brackets as :-

f (x) = y = (x + 1) / (x - 2)
y = (x + 1) / (x - 2)
y x - 2y = x + 1
( y - 1 ) x = 1 + 2 y
x = ( 1 + 2y ) / ( y - 1 )
g (y) = ( 1 + 2y ) / ( y - 1 )
g (x) = (1 + 2x ) / ( x - 1)