Transposition as part of a laplace transform

[Trespaser5]

I am doing a laplace transform as part of a coursework assignment. I have some example transpositions that are relevant to the question I am answering but I can't see how the author has got from one arrangement to the next.



2. Homework Equations

He has given

1/(s^2(τs+1)) = 1/(τs^2(s+1/τ))

Is there a rule of transposition I don't know about ? How has he created two instances of τ and made 1/τ ? I know I could follow it blindly but I'd really like to know how he got there.

Thank you in advance

 

[LCKurtz]

I am doing a laplace transform as part of a coursework assignment. I have some example transpositions that are relevant to the question I am answering but I can't see how the author has got from one arrangement to the next.



2. Homework Equations

He has given

1/(s^2(τs+1)) = 1/(τs^2(s+1/τ))

Is there a rule of transposition I don't know about ? How has he created two instances of τ and made 1/τ ? I know I could follow it blindly but I'd really like to know how he got there.

Thank you in advance

When you use partial fractions you are looking for factors like $s^2$ or $(s+a)$ in the denominator. Your denominator has $\tau s + 1$ as a factor. To get it into the $s+a$ form, you factor out the $\tau$ getting $\tau(s+\frac 1 \tau)$. The $\tau$ out in front doesn't hurt anything and what is left is in the proper form to expand in partial fractions to find the inverse.

 

[Mark44]

Questions about Laplace transforms should be posted in the Calculus & Beyond section, not in the Precalc section. I am moving this thread to that section.