Question 131917
{{{(9t^2+9t)/(45t^2+81t)}}} Start with the given expression


{{{(9t(t+1))/(45t^2+81t)}}}   Factor {{{9t^2+9t}}} to get {{{9t(t+1)}}} 


{{{(9t(t+1))/(9t(5t+9))}}}   Factor {{{45t^2+81t}}} to get {{{9t(5t+9)}}} 


{{{(cross(9t)(t+1))/(cross(9t)(5t+9))}}}   Cancel like terms



{{{(t+1)/(5t+9)}}} Simplify



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Answer:

So {{{(9t^2+9t)/(45t^2+81t)}}} simplifies to {{{(t+1)/(5t+9)}}}


In other words, {{{(9t^2+9t)/(45t^2+81t)=(t+1)/(5t+9)}}}