# Tricky Algebra question

Discussion in 'Math' started by Jess_88, Jun 3, 2011.

1. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
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

2. ### jegues Well-Known Member

Sep 13, 2010
735
43
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 likes this.
3. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
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

4. ### BillO Distinguished Member

Nov 24, 2008
988
136
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:

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

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

Last edited: Jun 3, 2011
Jess_88 likes this.
5. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
aaah! I got it!

6. ### victorhugo289 Member

Aug 24, 2010
49
3
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...

Last edited: Jun 3, 2011
7. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
Its a Laplace transformation question. I need to arrange the equation in terms of Vo and use partial fraction to determine the Laplace transformation.

8. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,052
310
You "just" need to find the common abominator.
Eric