SOLUTION: Simplify {{{((s^2+3s)/(s^2+2s-3))/((s)/(s+1))}}}

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Simplify {{{((s^2+3s)/(s^2+2s-3))/((s)/(s+1))}}}      Log On

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Question 125836: Simplify

%28%28s%5E2%2B3s%29%2F%28s%5E2%2B2s-3%29%29%2F%28%28s%29%2F%28s%2B1%29%29
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28s%5E2%2B3s%29%2F%28s%5E2%2B2s-3%29%29%2F%28%28s%29%2F%28s%2B1%29%29 Start with the given expression

%28%28s%5E2%2B3s%29%2F%28s%5E2%2B2s-3%29%29%2A%28%28s%2B1%29%2Fs%29 Multiply the first fraction by the reciprocal of the second fraction


%28%28s%28s%2B3%29%29%2F%28s%5E2%2B2s-3%29%29%28%28s%2B1%29%2F%28s%29%29 Factor s%5E2%2B3s to get s%28s%2B3%29

%28%28s%28s%2B3%29%29%2F%28%28s%2B3%29%28s-1%29%29%29%28%28s%2B1%29%2F%28s%29%29 Factor s%5E2%2B2s-3 to get %28s%2B3%29%28s-1%29


s%28s%2B3%29%28s%2B1%29%2F%28s%2B3%29%28s-1%29%28s%29 Combine the fractions


%28cross%28s%29%2Across%28%28s%2B3%29%29%28s%2B1%29%29%2Fcross%28%28s%2B3%29%29%28s-1%29cross%28s%29 Cancel like terms


%28s%2B1%29%2F%28s-1%29 Simplify


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Answer:

So %28%28s%5E2%2B3s%29%2F%28s%5E2%2B2s-3%29%29%2F%28%28s%29%2F%28s%2B1%29%29 simplifies to %28s%2B1%29%2F%28s-1%29. In other words %28%28s%5E2%2B3s%29%2F%28s%5E2%2B2s-3%29%29%2F%28%28s%29%2F%28s%2B1%29%29=%28s%2B1%29%2F%28s-1%29