In my math book it says: −1(s2×(s+1))=−1(s+1)−1(s2)+1s
But I just can't wrap my head around it! How do they get from left to right?
Can somebody please help me? :)
Thanks so much if you can :)
+130477 This is known as a partial fraction decomposition....let's look at this......
-1 / [ s^2 * ( s + 1) ] ....we can split this up as
-1 / [ s^2 * (s + 1)] = A / s + B /s^2 + C / (s + 1) ...where A, B and C are coefficients to be determined
Multiply both sides by [ s^2 * (s + 1)] ....so we have......
-1 = As(s + 1) + B (s + 1) + Cs^2 simplify (factor) the right side like so .....
-1 = (A + C)s^2 + (A + B)s + B then, equating coefficients sets up the following system
B = -1
A + B = 0 which implies that A = 1
A + C = 0 which implies that C = -1 so we have
-1 / [ s^2 * (s + 1)] = 1 / s - 1 /s^2 - 1 / (s + 1) which is essentially the same as your result
If you're unfamiliar with this technique, here's a good primer........http://www.purplemath.com/modules/partfrac.htm
"How do they get from left to right?"
You are trying wrong way.. it's simple to get from right to left.
- 1 / (s + 1) - 1 / s^2 + 1/s = - s^2 / (s^2(s+1)) + (- s - 1)/(s^2(s+1)) + (s^2 + s)/(s^2(s+1))
= - 1 / (s^2(s+1))
+130477 This is known as a partial fraction decomposition....let's look at this......
-1 / [ s^2 * ( s + 1) ] ....we can split this up as
-1 / [ s^2 * (s + 1)] = A / s + B /s^2 + C / (s + 1) ...where A, B and C are coefficients to be determined
Multiply both sides by [ s^2 * (s + 1)] ....so we have......
-1 = As(s + 1) + B (s + 1) + Cs^2 simplify (factor) the right side like so .....
-1 = (A + C)s^2 + (A + B)s + B then, equating coefficients sets up the following system
B = -1
A + B = 0 which implies that A = 1
A + C = 0 which implies that C = -1 so we have
-1 / [ s^2 * (s + 1)] = 1 / s - 1 /s^2 - 1 / (s + 1) which is essentially the same as your result
If you're unfamiliar with this technique, here's a good primer........http://www.purplemath.com/modules/partfrac.htm
