(1)/(2a^(2)+3)+(1)/(2b^(2)+3)+(1)/(2c^(2)+3)

asked by guest
on Sep 20, 2024 at 6:18 am



You asked:

Evaluate the expression: \(\frac{1}{2 \cdot {a}^{2} + 3} + \frac{1}{2 \cdot {b}^{2} + 3} + \frac{1}{2 \cdot {c}^{2} + 3}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{1}{2 \cdot {a}^{2} + 3} + \frac{1}{2 \cdot {b}^{2} + 3} + \frac{1}{2 \cdot {c}^{2} + 3} = \frac{1}{2 c^{2} + 3} + \frac{1}{2 b^{2} + 3} + \frac{1}{2 a^{2} + 3} \)

Factored

\[\frac{1}{2 \cdot {a}^{2} + 3} + \frac{1}{2 \cdot {b}^{2} + 3} + \frac{1}{2 \cdot {c}^{2} + 3} = \frac{4 a^{2} b^{2} + 4 a^{2} c^{2} + 12 a^{2} + 4 b^{2} c^{2} + 12 b^{2} + 12 c^{2} + 27}{\left(2 a^{2} + 3\right) \left(2 b^{2} + 3\right) \left(2 c^{2} + 3\right)}\]

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