proving that $\frac{1}{\sqrt{a}+\sqrt{b}}+\frac{1}{\sqrt{b}+\sqrt{c}}+\frac{1}{\sqrt{c}+\sqrt{d}}=\frac{3}{\sqrt{a}+\sqrt{d}}$ for any A.P.

if $a,b,c,d$ are an arithmetic progression (in that order), prove that

I made $n$ the common difference of $a,b,c,d$; so

$a=a$

$b=a+n$

$c=a+2n$

$d=a+3n$

I tried to replace the terms with those, anyways i squared both equalities but i didn 't get nothing since i'm pretty bad with square roots. I'm looking for some hints or properties that can be useful. Thanks

if $a,b,c,d$ are an arithmetic progression (in that order), prove that

I made $n$ the common difference of $a,b,c,d$; so

$a=a$

$b=a+n$

$c=a+2n$

$d=a+3n$

I tried to replace the terms with those, anyways i squared both equalities but i didn 't get nothing since i'm pretty bad with square roots. I'm looking for some hints or properties that can be useful. Thanks