As #(x-1)/(x+2)<0#, #x# cannot take value of #-2#.

From this we know that the product #(x-1)/(x+2)# is negative. It is apparent that sign of binomials #(x+2)# and #x-1# will change around the values #-2# and #1# respectively. In sign chart we divide the real number line using these values, i.e. below #-2#, between #-2# and #1# and above #1# and see how the sign of #(x-1)/(x+2)# changes.

**Sign Chart**

#color(white)(XXXXXXXXXXX)-2color(white)(XXXXX)1#

#(x+2)color(white)(XXX)-ive color(white)(XXXX)+ive color(white)(XXXX)+ive#

#(x-1)color(white)(XXX)-ive color(white)(XXXX)-ive color(white)(XXXX)+ive#

#(x-1)/(x+2)color(white)(XXX)+ive color(white)(XXX)-ive color(white)(XXXX)+ive#

It is observed that #(x-1)/(x+2) < 0# between #-2# and #1# i.e. #-2 < x < 1#, which is the solution for the inequality.