(81 x 3x+13^{x+1} -9 x 3x3^{x} ) / (81 x 3x+23^{x+2} -3 x 3x+23^{x+2} )

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on Apr 05, 2025 at 1:07 am



You asked:

Evaluate the expression: 81x⋅3x+1−9x⋅3x81x⋅3x+2−3x⋅3x+2\frac{81 x \cdot {3}^{x + 1} - 9 x \cdot {3}^{x}}{81 x \cdot {3}^{x + 2} - 3 x \cdot {3}^{x + 2}}

MathBot Answer:

Evaluated



81x⋅3x+1−9x⋅3x81x⋅3x+2−3x⋅3x+2=3−x−2(−9⋅3xx+81⋅3x+1x)78x\displaystyle \frac{81 x \cdot {3}^{x + 1} - 9 x \cdot {3}^{x}}{81 x \cdot {3}^{x + 2} - 3 x \cdot {3}^{x + 2}} = \frac{3^{- x - 2} \left(- 9 \cdot 3^{x} x + 81 \cdot 3^{x + 1} x\right)}{78 x}

Expanded

81x⋅3x+1−9x⋅3x81x⋅3x+2−3x⋅3x+2=13\frac{81 x \cdot {3}^{x + 1} - 9 x \cdot {3}^{x}}{81 x \cdot {3}^{x + 2} - 3 x \cdot {3}^{x + 2}} = \frac{1}{3}

Factored

81x⋅3x+1−9x⋅3x81x⋅3x+2−3x⋅3x+2=3⋅3x3−x−2\frac{81 x \cdot {3}^{x + 1} - 9 x \cdot {3}^{x}}{81 x \cdot {3}^{x + 2} - 3 x \cdot {3}^{x + 2}} = 3 \cdot 3^{x} 3^{- x - 2}

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