Partial Fraction Help: Solving Equations with 1/(s(1+RCs))

[kokkie_d]

Homework Statement

Hi,

I have the following problem. These two equations are the same but I can not find the right route from one to the other. Is there someone who can help me?
In other words, I start with the equation on the left and want to end with the equation on the right.

Homework Equations

1/(s(1+RCs)) = 1/s - 1/(s + 1/RC)

The Attempt at a Solution

1/(s(1+RCs)) multiply top and bottom by 1-RCs
= (1-RCs) / (s * (1+RCs) * (1-RCs))
= (1-RCs) / (s - (RCs^2) * s)
= (1 / s) - 1 / (RCs*s)

Cheers

 

[Mark44]

Homework Statement

Hi,

I have the following problem. These two equations are the same but I can not find the right route from one to the other. Is there someone who can help me?
In other words, I start with the equation on the left and want to end with the equation on the right.

Homework Equations

1/(s(1+RCs)) = 1/s - 1/(s + 1/RC)

The Attempt at a Solution

1/(s(1+RCs)) multiply top and bottom by 1-RCs
= (1-RCs) / (s * (1+RCs) * (1-RCs))
= (1-RCs) / (s - (RCs^2) * s)
= (1 / s) - 1 / (RCs*s)

Cheers

Start from the right side. Multiply the first fraction by (s + 1/RC) over itself. Multiply the second fraction by s over itself.

 

[MisterMan]

Alternatively to the way Mark44 did it, you could also split the fraction you have on the left up into two fractions. Then multiply the separate fractions by the opposing denominator, that's a starting point. See if you can work it out from there.