Partial Fraction - Cover up Method
The cover up method is not taught in the Shing Lee Additional Mathematics and Pan Pacific Additional Mathematics textbooks.
The cover method can only be used when the factors in the denominators are linear.
Example
If (12x - 6) / [(x+2)(x-4)] = A/(x+2) + B/(x-4), find the value of A and of B.
Step 1 : To find the value of A
Cover up (x+2), substitute x = -2 into (12x - 6) / (x - 4) = (12(-2) - 6) / (-2 -4) = 5
So, A = 5
Step 2 : To find the value of B
Cover up (x-4), substitute x = 4 into (12x - 6) / (x +2) = (12(4) - 6) / (4+2) = 7
So, B = 7
Hence, (12x - 6) / [(x+2)(x-4)] = A/(x+2) + B/(x-4)
(12x - 6) / [(x+2)(x-4)] = 5/(x+2) + 7/(x-4)
Thank you for your kind attention.
Regards,
ahm97sic
It is thought in the PanPac book, page 96, EG 13, 14, 15
they all use the cover mathood wad ... .. =.=
btw, the cover-up methood is the subsitution methood... ... in the SingLee TB, pg 66, methood 2
So any prob with it?
Hi tr@nsp0rt_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
well done ahm97sic
o.O okay... ... thankx for that comparison...
but by missing this one step.. will it made more careless mistake?
but anyway that's for that methood ^^
this is what I always teach my students: use quick checks method for such algebra manipulations
how? Sub in a simple value, say 0
Make sure that the result of subbing in for the original one and the final answer is the same
To confirm, maybe sub in 1 or 2 as well. If you get the same answer for before and after manipulations, you are 99% correct.
Such methods can be utilised for many other topics as well, especially those using algebras ;)