It is known that two straight lines are:

l 1:a 1x+b 1y+c 1 = 0；

l2:A2x+B2y+C2=0

So: Two straight lines are parallel.

Two straight lines are vertical < = >A 1A2+B 1B2=0.

Therefore, for the straight lines (a+2)x+( 1-a)y- 1=0 and (a- 1)x+(2a+3)y+2=0,

Two straight lines are vertical < = > (a+2) (a-1)+(1-a) (2a+3) = 0.

This gives a= 1, or a=- 1.

Note: The above method is applicable to the general equation of straight line. If the linear equation is not general, please convert it into a general equation.

Reference: Chapter 3 "Equation of Straight Line and Circle" is a compulsory part of senior high school mathematics teaching.