Boolean Network Simplification using Satisfiability Don't care Conditions
$$ y=abx+a'cx $$
replacing \$x=a′+b\$ &amp; reducing further:
$$ y = ab +a'c + a'cb $$
Using rule:  \$A+A'B = A+B\$
$$y= ab +a'c $$
$$y=  aa' + ab +a'c $$
$$y=  ax +a'c $$

You can get the same with K-map also.