((8x^3-27)(4x^2+6X+9)^-1)

asked by guest
on Oct 22, 2024 at 4:25 am



You asked:

Evaluate the expression: \(\left(8 \cdot {x}^{3} - 27\right) \cdot {\left( 4 \cdot {x}^{2} + 6 X + 9 \right)}^{-1}\)

MathBot Answer:

Evaluated



\(\displaystyle \left(8 \cdot {x}^{3} - 27\right) \cdot {\left( 4 \cdot {x}^{2} + 6 X + 9 \right)}^{-1} = \frac{8 x^{3} - 27}{6 X + 4 x^{2} + 9} \)

Expanded

\[\left(8 \cdot {x}^{3} - 27\right) \cdot {\left( 4 \cdot {x}^{2} + 6 X + 9 \right)}^{-1} = \frac{8 x^{3}}{6 X + 4 x^{2} + 9} - \frac{27}{6 X + 4 x^{2} + 9}\]

Factored

\[\left(8 \cdot {x}^{3} - 27\right) \cdot {\left( 4 \cdot {x}^{2} + 6 X + 9 \right)}^{-1} = \frac{\left(2 x - 3\right) \left(4 x^{2} + 6 x + 9\right)}{6 X + 4 x^{2} + 9}\]

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