Algebra  Inequalities  Inequalities  variable in the denominator.
Test Yourself 1  Solutions.
Multiplication can create an x^{2} term. 
Hence the required domain is either:
Test a number in the original inequality  0 is easy and it is in the second domain above. We get 0 after substitution which is less than 3  so the inequality is not satisfied (sad). Hence the required domain is from 5 to 6. But the correct domain cannot include 5 because then the denominator would be 0  not generally a good thing!!! So our solution is 5 < x ≤ 6. 
Hence the required domain is either:
Test a number in the original inequality  0 is easy and it is in the first domain above. We get 1.5 after substitution which is greater than 1  so the inequality is satisfied (so be happy). Hence the required domain is from 1 to 2. The correct domain cannot include 2 because then the denominator would be 0  so the fraction would be undefined!!! So our solution is 1 ≤ x < 2. 
Multiplication can create an term greater than x^{2}. 
Hence the required domain is either:
Test a number in the original inequality  0 is easy and it is in the second domain above. We get 1.5 after substitution into the left side which is less than 0  so the inequality is satisfied (happy). So our solution is x ≤ 1 or 2 ≤ x ≤ 3. 

Where on the graph of y = log_{e} (x2) is the gradient of the curve greater than 1. 