Start with given equation
Switch the x and y variables
Now solve for y
x=(\frac{3+2y}{2-5y})(\frac{2-5y}{1}))
Multiply both sides by (2-5y)
Distribute the x on the left side
Get all y terms to one side
)
Factor out a y
}{(2+5x)})
Divide both sides by (2+5x)
Here's our inverse function. In other words
=\frac{-3+2x}{2+5x})
Check:
If we let x=1 and plugged it into we would get
If we plug in 
in for x into our inverse equation we should get y=1 out.
}{2+5(-5/3)})
So this verifies that is our answer. Hope all of this makes sense.