Tricky Algebra question

Jess_88

Joined Apr 29, 2011
174
Hey guys.
I was wondering if someone could show me the working out (simplification) for these two equation. This isn't a homework question... just study. If more information is needed... let me know

1)

2)

thanks guys

jegues

Joined Sep 13, 2010
733
Hey guys.
I was wondering if someone could show me the working out (simplification) for these two equation. This isn't a homework question... just study. If more information is needed... let me know

1)

2)

thanks guys
For 1,

$$\frac{5}{s+2} = \left( \frac{s+1}{2s+1} \right)V_{o}$$

$$\frac{ 5 \times (2s+1)}{(s+2)(s+1)} = V_{o}$$

$$\Rightarrow \frac{10s+5}{(s+2)(s+1)} = V_{o}$$

Or if you're confused by the first simplification,

$$\frac{V_{o}}{2s+1} + \frac{V_{o}}{2 + \frac{1}{s}}$$

$$= \left( \frac{1}{2s+1} + \frac{1}{\frac{2s+1}{s}} \right)V_{o}$$

$$= \left( \frac{1}{2s+1} + \frac{s}{2s+1} \right)V_{o}$$

$$= \left( \frac{s+1}{2s+1} \right)V_{o}$$

If I have time later I will look through the 2nd one as well. (It's the same type of algebra, nothing difficult)

Jess_88

Joined Apr 29, 2011
174
ah thats great!
Yeah I understand its simple... I just haven't worked with such fractions in a long time.
If you do have time to do the second one later that would be great.
Thanks for the help

BillO

Joined Nov 24, 2008
990
You need to take it in steps. First step is to eliminate the 2/S denominator by multiplying both the top and bottom of the second term with S/2

Such that we have:

$$\frac{3}{S} -Vo\ \ -\frac{1}{2}-\frac{SVo}{2}\ \ +\frac{4}{S}-Vo\ \ =\ \ 0$$

Collecting the terms with Vo on one side we get

$$2Vo+\frac{S}{2}Vo\ \ =\ \ \frac{7}{S} - \frac{1}{2}$$

Multiplying both sides by 2 and simplifying:

$$\Rightarrow\ \ \ \ Vo(4+S)\ \ =\ \ \frac{14-S}{S}$$

$$\Rightarrow\ \ \ \ Vo\ \ =\ \ \frac{14-S}{S(S+4)}$$

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Jess_88

Joined Apr 29, 2011
174
aaah! I got it!

victorhugo289

Joined Aug 24, 2010
49
I thought you had to solve for something in here, but this is a plug-in-the-values type of equation.
Not much simplification, really.
It's more like a formula. It is a formula...

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Jess_88

Joined Apr 29, 2011
174
I thought you had to solve for something in here, but this is a plug-in-the-values type of equation.
Not much simplification, really.
It's more like a formula. It is a formula...
Its a Laplace transformation question. I need to arrange the equation in terms of Vo and use partial fraction to determine the Laplace transformation.

KL7AJ

Joined Nov 4, 2008
2,229
You "just" need to find the common abominator.
Eric