(6x^2 + 24x) / (2x^2 + 5x -12) รท (4x^2 - 9)/(15x^2)

asked by guest
on Sep 22, 2024 at 4:14 pm



You asked:

Evaluate the expression: \(\frac{\frac{\frac{6 \cdot {x}^{2} + 24 x}{2 \cdot {x}^{2} + 5 x - 12}}{4 \cdot {x}^{2} - 9}}{15 \cdot {x}^{2}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{\frac{6 \cdot {x}^{2} + 24 x}{2 \cdot {x}^{2} + 5 x - 12}}{4 \cdot {x}^{2} - 9}}{15 \cdot {x}^{2}} = \frac{6 x^{2} + 24 x}{15 x^{2} \cdot \left(4 x^{2} - 9\right) \left(2 x^{2} + 5 x - 12\right)} \)

Expanded

\[\frac{\frac{\frac{6 \cdot {x}^{2} + 24 x}{2 \cdot {x}^{2} + 5 x - 12}}{4 \cdot {x}^{2} - 9}}{15 \cdot {x}^{2}} = \frac{6 x^{2}}{120 x^{6} + 300 x^{5} - 990 x^{4} - 675 x^{3} + 1620 x^{2}} + \frac{24 x}{120 x^{6} + 300 x^{5} - 990 x^{4} - 675 x^{3} + 1620 x^{2}}\]

Factored

\[\frac{\frac{\frac{6 \cdot {x}^{2} + 24 x}{2 \cdot {x}^{2} + 5 x - 12}}{4 \cdot {x}^{2} - 9}}{15 \cdot {x}^{2}} = \frac{2}{5 x \left(2 x - 3\right)^{2} \cdot \left(2 x + 3\right)}\]

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