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Question
Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
Solution
`[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`
= `[ 3 xx (3^2)^(n + 1) - 3^2 xx 3^(2n)]/[ 3 xx 3^(2n + 3) - (3^2)^(n + 1)]`
= `[ 3^( 1 + 2n + 2) - 3^( 2 + 2n )]/[3^(1 + 2n + 3) - 3^( 2n + 2 )]`
= `[ 3^( 3 + 2n ) - 3^( 2 + 2n )]/[3^(4 + 2n) - 3^( 2n + 2 )]`
= `[ 3^(2n)( 3^3 - 3^2 )]/[3^(2n)(3^4 - 3^2)]`
= `[ 27 - 9 ]/[ 81 - 9 ]`
= `18/72`
= `1/4`
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