FRACTIONAL INEQUALITIES The Step to solving of fractional inequality : Find the x values which cause the numerator and denominator are zero Put them on the number line Sign every part of the number line ( either positive or negative ) Remember with “ the denominator isn’t equal zero Find the solution set

Example The SS is { x/x ≤ -2 or x>1, x Є R } 1. Find the solution set : step 1 X + 2 = 0,→ x = -2 X - 1= 0, → x = 1 Step 2 -2 1 Step 3 +++ ---- ++++ Step 4 ? ( x ≠ 1) step 5 The SS is { x/x ≤ -2 or x>1, x Є R }

Example The SS { x/ -2 ≤ x ≤ 2 or 3 < x < 4,xЄ R 2. +++ ---- +++ --- +++ -2 2 3 4 The SS { x/ -2 ≤ x ≤ 2 or 3 < x < 4,xЄ R

example 3. The numerator doesn’t have the values of x which cause the numerator is zero X2 + 1 is definite positive ------ ++++++ -------- -4 4 The SS is { x / x < -4 or x > 4, x Є R }

example The SS is { x/x < ½ or x >3, x Є R } 4. ------ ++++ -------- ½ 3 The SS is { x/x < ½ or x >3, x Є R }