Please tell me how can I simplify this...?

Question

#{3^n+3^(n+1)}/{3^n+3^(n-1)#

Please show all the steps and explain them :)

950 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-28T11:28:58

#{3^n+3^(n+1)}/(3^n+3^(n-1)) = 3#

#{3^n+3^(n+1)}/(3^n+3^(n-1))#

#={3^n+3^nxx3^1}/(3^n+3^n/3^1)#

Factor #3^n#'s from top and bottom :

#={3^n(1+3)}/(3^n (1 + 1/3))#

#= (1+3)/(1 + 1/3)#

#= 4/(4/3) = 3#

Answer 2 · 2018-04-28T11:44:31

#3#

#"factor the numerator and denominator"#

#rArr(3^n(1+3^1))/(3^n(1+3^-1))#

#=(cancel(3^n)(1+3))/((cancel(3^n)(1+1/3))#

#=4/(4/3)=4xx3/4=3#