How do you multiply #((t+2)^3/(t+1)^3(t^2+2t+1)/(t^2+4t+4)(t+1)/(t+2)) #?

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Answer 1 · 2018-04-13T21:13:03

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First, we start by factoring #(t^2+2t+1)/(t^2+4t+4)#

#((t+1)^2)/(t^2+4t+4)# Factoring the numerator first.

#((t+1)^2)/((t+2)^2)# Then factoring the denominator.

Now, it is easy to multiply:

#(t+1)^2/(t+2)^2*(t+1)/(t+2) = (t+1)^3/(t+2)^3#

Finally, we can multiply

#(t+1)^3/(t+2)^3*(t+2)^3/(t+1)^3 = ((t+1)^3*(t+2)^3)/((t+1)^3*(t+2)^3) = 1/1 = 1#

How do you multiply #((t+2)^3/(t+1)^3*(t^2+2t+1)/(t^2+4t+4)*(t+1)/(t+2)) #?