hi deep

see first condition (x-1/x+5)*1/(x²-36) >0 (as the expression is within log)

second condition  log_0.4 (x-1/x+5)*1/(x²-36) >=0  (as this expression is within root)

this implies (x-1/x+5)*1/(x²-36) <=1

 

therefore from both the two  conditions (x-1/x+5)*1/(x²-36) >0 & <=1

solve the inequalities two get the answer