Is There an Error in the r+-r- Expression?

[aaaa202]

Greeetings, yesterday I had to do the attached assignment but I ran into a problem. It is not so much about how to solve the exercise but rather about how to approximate the term:
r₊-r_-
My solutions notes writes this as:
r₊-r_- = Lx/z₀
Is it just me or is there something wrong with this expression: How did my teacher arrive at that from:
r₊-r_- = √((x-L/2)²+y²+z₀²) - √((x+L/2)²+y²+z₀²)

 

[voko]

Divide everything by Zo then use the linear approximation of the square root.

 

[aaaa202]

hmm okay I think I got it. I just find it weird that there is no dependence on y while there is a dependence of x? Why is that intuitively?

 

[voko]

Intuitively that is because of the asymmetry along the x-axis.