Chứng minh rằng: \(\frac{a^3}{a+b} + \frac{b^3}{b+c} + \frac{c^3}{c+a} = \frac{a^2b}{a+b} + \frac{b^2c}{b+c} + \frac{c^2a}{c+a}\)

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Bài 6. Chứng minh rằng:
a) \(\frac{a^3}{a+b} + \frac{b^3}{b+c} + \frac{c^3}{c+a} = \frac{a^2b}{a+b} + \frac{b^2c}{b+c} + \frac{c^2a}{c+a}\)
b) \(\left( \frac{2a + 2b - c}{3} \right) + \left( \frac{2b + 2c - a}{3} \right) + \left( \frac{2c + 2a - b}{3} \right) = a^2 + b^2 + c^2\)