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# (3^(4n)-3^(2n))\ (3^(3n) + 3^(2n))

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(3^(4n)-3^(2n))\ (3^(3n) + 3^(2n))

Guest Jul 29, 2015

#1
+18829
+13

$$\small{\text{ \begin{array}{rcl} \dfrac{ 3^{4n}-3^{2n} } { 3^{3n} + 3^{2n} } \\ &=& \dfrac{ 3^{2n+2n}-3^{2n} } { 3^{2n+n} + 3^{2n} } \\\\ &=& \dfrac{ 3^{2n}3^{2n}-3^{2n} } { 3^{2n}3^{n} + 3^{2n} } \\\\ &=& \dfrac{ 3^{2n} (3^{2n}-1) } { 3^{2n} (3^{n} + 1) } \\\\ &=& \dfrac{ 3^{2n}-1 } { 3^{n}+1 } \\\\ &=& \dfrac{ (3^{n}-1)(3^{n}+1) } { 3^{n}+1 } \\\\ \mathbf{ \dfrac{ 3^{4n}-3^{2n} } { 3^{3n} + 3^{2n} } }&\mathbf{=} & \mathbf{3^{n}-1} \end{array} }}$$

heureka  Jul 29, 2015
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#1
+18829
+13
$$\small{\text{ \begin{array}{rcl} \dfrac{ 3^{4n}-3^{2n} } { 3^{3n} + 3^{2n} } \\ &=& \dfrac{ 3^{2n+2n}-3^{2n} } { 3^{2n+n} + 3^{2n} } \\\\ &=& \dfrac{ 3^{2n}3^{2n}-3^{2n} } { 3^{2n}3^{n} + 3^{2n} } \\\\ &=& \dfrac{ 3^{2n} (3^{2n}-1) } { 3^{2n} (3^{n} + 1) } \\\\ &=& \dfrac{ 3^{2n}-1 } { 3^{n}+1 } \\\\ &=& \dfrac{ (3^{n}-1)(3^{n}+1) } { 3^{n}+1 } \\\\ \mathbf{ \dfrac{ 3^{4n}-3^{2n} } { 3^{3n} + 3^{2n} } }&\mathbf{=} & \mathbf{3^{n}-1} \end{array} }}$$