Question 125836
{{{((s^2+3s)/(s^2+2s-3))/((s)/(s+1))}}} Start with the given expression


{{{((s^2+3s)/(s^2+2s-3))*((s+1)/s)}}} Multiply the first fraction by the reciprocal of the second fraction



{{{((s(s+3))/(s^2+2s-3))((s+1)/(s))}}}   Factor {{{s^2+3s}}} to get {{{s(s+3)}}} 


{{{((s(s+3))/((s+3)(s-1)))((s+1)/(s))}}}   Factor {{{s^2+2s-3}}} to get {{{(s+3)(s-1)}}} 



{{{s(s+3)(s+1)/(s+3)(s-1)(s)}}} Combine the fractions



{{{(cross(s)*cross((s+3))(s+1))/cross((s+3))(s-1)cross(s)}}} Cancel like terms



{{{(s+1)/(s-1)}}} Simplify



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Answer:


So {{{((s^2+3s)/(s^2+2s-3))/((s)/(s+1))}}} simplifies to {{{(s+1)/(s-1)}}}. In other words {{{((s^2+3s)/(s^2+2s-3))/((s)/(s+1))=(s+1)/(s-1)}}}