Hi [email protected]_F3V3R,
There are differences and similarities between the 2
methods.
The cover up method is just to let the students know that
there is another way to solve partial fraction questions when the
factors in the denominators are linear.
This does not mean that the cover up method is better than the
substitution method or vice versa.
(It is just like there are many
ways (long division, multiply and equate, inverted L,
inspection and factorise, calculator (using MOE approved calculator
Casio FX 95 MS or Sharp EL 509WS) method) to solve the cubic
equation eg 2x^3 + 3x^2 - 11x
- 6 = 0)
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
Thank you for your kind attention.
Regards,
ahm97sic