# Is there a more simple and less confusing way of solving laplace-tranformation equations?

The picture I have shared below shows the laplace transform of the circuit. The calculations shown are really simplified. I know how to do laplace transforms but the problem is they are super long and gets confusing after sometime. For example the equation I've marked with a blue star is really simplified but when I try to solve it, it gets really long and confusing. I've tried using my calculator (Casio fx-991EX Classwiz) for it but I can't seem to use anything instead of the letter s (for s-domain). I would really appreciate it if someone could tell me a simple and less confusing way to do laplace transforms. Maybe even show me how to use my calculator for it because I can't find any sources for laplace transformation done with my calculator. Thank you in advance.

## Edit: My attempt at solving was to just multiply everything and try to simplify them, but I noticed it was becoming a long equation.

• Could you please show how you tried to solve the equation denoted by the blue asterisk? Otherwise, it'll be very hard to help you. Commented Jun 17, 2021 at 11:41
• It's an university exercise, so I doubt you can use a calculator. At least when I was a student it was forbidden. I do suspect that any other form of the result is not valid, so keep doing the math exercise and forget about computer and calculator. Commented Jun 17, 2021 at 11:41
• @uriyaba I've added my attempt at solving. It doesn't show the whole solution because it was getting super long but my thought was to just do all the multiplication and just simplifying it. Commented Jun 17, 2021 at 12:00
• @MarkoBuršič we can't use programmable calculators but the calculator I am using is allowed. So, if I can figure out a way to just find an alternative instead of the letter 's', I can easily solve them. I've tried using 'x' instead of 's' but it just does the calculation as if it is a variable, not as a place holder. Commented Jun 17, 2021 at 12:03

Go and study partial fractions is my recommendation. However, there is a math site that does solve PFs for you and comes up with this answer when converting $$\\dfrac{1}{x(x+8000)(x+20000)}\$$: -
$$\frac{1}{160000000x}-\frac{1}{96000000\left(x+8000\right)}+\frac{1}{240000000\left(x+20000\right)}$$