a( ax + 1) = x(a + 2) + 2
<=>a2x+a=xa+2x+2
<=>a2x-xa-2x=2-a
<=>x.(a2-a-2)=2-a
<=>x=\(\frac{2-a}{a^2-a-2}=\frac{-\left(a-2\right)}{a^2-2a+a-2}=\frac{-\left(a-2\right)}{a.\left(a-2\right)+\left(a-2\right)}=\frac{-\left(a-2\right)}{\left(a-2\right)\left(a+1\right)}=\frac{-1}{a+1}\)