Easy expression, I’m stuck here This is an expression obtained for resolving a circuit.
I tried for 1 hour now and I’m close but I’m doing something wrong. 
I’m trying to find detA. (details under the photo)
I’m new to this so be kind with me :) 

detA where A is the first matrice
$((1/x)+(1/y))*((1/y)+(1/z))$
I came up with this:
$(1/R1*R2)+(1/R1*R3)+(1/R2^2)+(1/R2*R3)-(-1/R2)^2 =$
$(1/R1)((1/R2)+(1/R3)) + (1/R2*R3)$
(note, maybe the parentheses around fractions are useless)
There are some similarities, it can be random.

Recall that
$$AV=J \implies V=A^{-1}J$$
and
$$A=\begin{pmatrix}a & b \\
c & d \end{pmatrix}\implies A^{-1}=\frac{1}{ad-bc}\begin{pmatrix}d & -b \\
-c & a \end{pmatrix}$$
with
$$\det (A)=\left(\frac1{R_1}+\frac1{R_2}\right)\left(\frac1{R_2}+\frac1{R_3}\right)-\frac1{R_2^2}=\frac1{R_1R_2}+\frac1{R_2R_3}+\frac1{R_3R_1}=\frac{R_1+R_2+R_3}{R_1R_2R_3}$$
