Find the inverse of x-2/x+5?

Question

Find the inverse of x-2/x+5?

Answer 1

Inverse of

y = (x-2)/(x+5)

First we swap the x and y

x = (y-2)/(y+5)

Multiply both sides by (y+5)

x(y+5) = y-2

Expand the left side

xy + 5x = y-2

Move the y to the left and the 5x to the right

xy-y = -5x-2

Factor the y out on the left (and clean up the sign on the right)

y(x-1) = -(5x+2)

Isolate the y by dividing out the bracketed term on the left

y = -(5x+2)/(x-1)

Pat yourself on the back ;)

Answer 2

(x^2 - 2 + 5x)/2