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The algebra techniques that you will use in ch 6 include 
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\hskip 1.1in partial fractions, 
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\hskip 1.1in  completing the square,
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\hskip 1.1in  adding 0, and 
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\hskip 1.1in multiplying by 1.

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1.  Look at denominator
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i.)  Does your denominator equal one of the following?
$s^n$, $s - a$, $s^2 \pm a^2$,
If so, use the appropriate formula.

ii.)  Can you factor denominator over the reals?  If so, factor and use partial fractions.

iii.)  Do you need to complete the square?
Example:  
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$10s^2 + 60s + 91 = 10(s^2 + 6s) + 91$
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\hskip .99in $= 10(s^2 + 6+ 9 - 9) + 91$
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\hskip .99in $= 10(s^2 + 6+ 9 ) -90 + 91$
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\hskip .99in $ = 10(s+3)^2 +1$

2.  Look at the numerator
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i.)  Do you need $s-a$?  Try adding 0.  For example to make $s + {3 \over 2}$ appear in $5s + 21$:
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\centerline{$5s + 21 = 5(s + {3 \over 2}) - {15 \over 2} + 21 = 5(s + {3 \over 2}) + {27 \over 2}$}


ii)  Do you need $b$?  Try multiplying by 1.  For example, if you need ${\sqrt{7 \over 4}} $, but you have 
${27 \over 2}$:
~~~~
${27 \over 2} = {27 \over 2}{\sqrt{4 \over 7}} {\sqrt{7 \over 4}} $

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\hskip -1.in  \includegraphics[width=4.8in]{LaPlace.pdf}


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