# 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