2(x squared plus 3/2 y squared) multiplied by -2/3 (6x squared minus 3y squared plus 5)

asked by guest
on Nov 18, 2024 at 10:25 pm



You asked:

Evaluate the expression: \(2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3 \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle 2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3 \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right)} = - \frac{4 \left(x^{2} + \frac{3 y^{2}}{2}\right)}{18 x^{2} - 9 y^{2} + 15} \)

Expanded

\[2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3 \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right)} = - \frac{4 x^{2}}{18 x^{2} - 9 y^{2} + 15} - \frac{6 y^{2}}{18 x^{2} - 9 y^{2} + 15}\]

Factored

\[2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3 \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right)} = - \frac{2 \cdot \left(2 x^{2} + 3 y^{2}\right)}{3 \cdot \left(6 x^{2} - 3 y^{2} + 5\right)}\]

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