SOLUTION: Given that f(X)=2/X(X+1)(X+2) express f(X) in partial fractions Hense show that s4 3f(X)dx=In (27/25) Given that (X+1) and (x-2) are factors of the expression ax2-x2+ bx-a, find

Algebra ->  Equations -> SOLUTION: Given that f(X)=2/X(X+1)(X+2) express f(X) in partial fractions Hense show that s4 3f(X)dx=In (27/25) Given that (X+1) and (x-2) are factors of the expression ax2-x2+ bx-a, find       Log On


   

Question 1085784: Given that f(X)=2/X(X+1)(X+2) express f(X) in partial fractions
Hense show that s4 3f(X)dx=In (27/25)
Given that (X+1) and (x-2) are factors of the expression ax2-x2+ bx-a, find the value of the constant a and b .
Sense, find also the remainder when the expression is divided by (x-4).
Express as a single fraction 5/x+2-7/2x+3
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28x%28x%2B1%29%28x%2B2%29%29=A%2Fx%2BB%2F%28x%2B1%29%2BC%2F%28x%2B2%29
2=A%28x%2B1%29%28x%2B2%29%2BBx%28x%2B2%29%2BCx%28x%2B1%29
2=A%28x%5E2%2B3x%2B2%29%2BBx%5E2%2B2Bx%2BCx%5E2%2BCx
2=%28A%2BB%2BC%29x%5E2%2B%283A%2B2B%2BC%29x%2B2A
So then,
2A=2
A=1
which leaves
1%2BB%2BC=0
3%2B2B%2BC=0
Subtract the first equation from the second,
3%2B2B%2BC-1-B-C=0
2%2BB=0
B=-2
and finally,
1-2%2BC=0
-1%2BC=0
C=1
So,
2%2F%28x%28x%2B1%29%28x%2B2%29%29=1%2Fx-2%2F%28x%2B1%29%2B1%2F%28x%2B2%29