Help Arranging Laplace Equation for Test Prep

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SUMMARY

The discussion focuses on rearranging the Laplace equation derived from a circuit analysis. The original equation, Vo { 1/4000 + 1/(0.08S) + 1/(21000 + 10^9/(5S) } = 300/S, needs to be transformed into the form Vo = 12*(21S + 20*10^4) / {(S+10000)*(S+40000)}. The key challenge lies in simplifying the term 1/(21000 + 10^9/(5S)), which can be rewritten as 5S/(21000*5S + 10^9) to facilitate the rearrangement.

PREREQUISITES
  • Understanding of Laplace transforms and their applications in circuit analysis.
  • Familiarity with algebraic manipulation of rational expressions.
  • Knowledge of circuit theory, particularly in analyzing voltage and current relationships.
  • Proficiency in handling complex fractions and simplifying them.
NEXT STEPS
  • Study the process of rearranging complex fractions in algebra.
  • Learn about Laplace transform properties and their implications in circuit analysis.
  • Explore examples of circuit equations and their transformations for better understanding.
  • Practice solving similar Laplace equations to enhance problem-solving skills.
USEFUL FOR

Students preparing for tests in electrical engineering, circuit designers, and anyone looking to deepen their understanding of Laplace transforms in circuit analysis.

Patrick.Gh
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hello all. my question isn't about the solution, but more how the solution was obtained.

i have a circuit from which i obtained the following equation
Vo { 1/4000 + 1/(0.08S) + 1/(21000 + 10^9/(5S) } = 300/S

however the problem is, that i can't arrange it so that it becomes in the following form, from which i can get the solution.
Vo = 12*(21S + 20* 10^4) / {(S+10000)*(S+40000)}

if someone can help me by explaining step by step how this was done, i would be VERY grateful as i have a test coming up.
P.S: usually if the equation has 1 term in each denominator i have no problem in arranging it. its the 1/(21000+ 10^9/(5S)) that is giving me the trouble.
 
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[tex]\frac{1}{21000 + \frac{10^9}{5s}} = \frac{5s}{21000*5s+10^9}[/tex]
 

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