Question

Fractions...explain step by step

Answer 1

CASE 1: NON-REPEATED LINEAR FACTOR
When a linear factor ax + b appears once as a factor of the denominator, associate the partial fraction equal to A/(ax+b) .

CASE 2: REPEATED LINEAR FACTOR
When a linear factor ax + b appears nth times as a factor of the denominator, associate the partial fraction equal to Asub1/(ax+b) + Asub2/(ax+b)^2 + Asub3/(ax+b)^3 + ....... + Asubn/(ax+b)^n .

CASE 3: NON-REPEATED QUADRATIC FACTOR
When a quadratic factor ax^2 + bx + c appears once as a factor of the denominator, associate a partial fraction equal to Ax+B/(ax^2+bx+c) .

CASE 4: REPEATED QUADRATIC FACTOR
When a quadratic factor ax^2 + bx + c appears nth times as a factor of the denominator, associate a partial fraction equal to Asub1x+Bsub1/(ax^2+bx+c)
+ Asub2x+Bsub2/(ax^2+bx+c)^2 + Asub3x+Bsub3/(ax^2+bx+c)^3 + ....... + Asubnx+Bsubn/(ax^2+bx+c)^n .

Answer 2

are those like rules...ok let me show you where I need some clearance because I get what you have said I am looking for the "why do i do this" part..let me explain

I have attached step 1
how have we used \[(x-2)^{2}\] twice..thats what i dont understand

Answer 3

the first time it is (x-2) and the second time it is squared...why?

Answer 4

because it is a repeated linear factor so... we will use it twice in different exponent.

Answer 5

ok...now I get it!!!!!!!! Thanks!!!!!!!!!! :-) :)

Answer 6

you're welcome. :)