Cover up Method Substitution Method
Question Question
(12x - 6) / [(x+2)(x-4)] (12x - 6) / [(x+2)(x-4)]
= A/(x+2) + B/(x-4) = A/(x+2) + B/(x-4)
Step 1 Step 1
Cover up (x+2), Multiply throughout by the denominator
substitute x = -2 into (12x - 6) / (x - 4) [(x+2)(x-4)]
= (12(-2) - 6) / (-2 -4) = 5 12x - 6 = A(x-4) + B(x+2)
So, A = 5
Step 2 Step 2 (a)
Cover up (x-4), Substitute x = -2 into
substitute x = 4 into (12x - 6) / (x +2) 12x - 6 = A(x-4) + B(x+2)
= (12(4) - 6) / (4+2) = 7 12(-2) - 6 = A(-2-4) + B(-2+2)
So, B = 7 A = 5
Step 2 (b)
Substitute x = 4 into
12x - 6 = A(x-4) + B(x+2)
12(4) - 6 = A(4-4) + B(4+2)
B = 7