Question

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`\frac{ {9}^(x + 1) - {3}^(2x) }{4 * {3}^(2x - 1) } \\`
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ans : 6

Answer 1

`{ \qquad\qquad\huge\underline{{\sf Answer}}}`

Here we go ~

`\qquad \sf  \dashrightarrow \: \cfrac{9 {}^((x + 1)) - 3 {}^(2x) }{4 * 3 {}^((2x - 1)) }`

`\qquad \sf  \dashrightarrow \: \cfrac{3{}^(2(x + 1)) - 3 {}^(2x) }{4 * 3 {}^((2x - 1)) }`

`\qquad \sf  \dashrightarrow \: \cfrac{3{}^((2x + 2)) - 3 {}^(2x) }{4 * 3 {}^((2x - 1)) }`

here :

• 
  `{ \sf {3}^((2x+2))=({3}^(2x - 1))\sdot (3³)}`

• 
  `{ \sf {3}^((2x))=({3}^((2x - 1)))\sdot (3¹)}`

`\qquad \sf  \dashrightarrow \: \cfrac{3{}^((2x - 1))(3 {}^(3) - 3 {}^(1)) }{4 * 3 {}^((2x - 1)) }`

[ taking
`{ \sf {3}^((2x - 1)) }`common here ]

`\qquad \sf  \dashrightarrow \: \cfrac{27 {}^{} - 3 {}^{}}{4 }`

`\qquad \sf  \dashrightarrow \: \cfrac{24{}^{} {}^{}}{4 }`

`\qquad \sf  \dashrightarrow \: 6`