Please answer this question..??

Dear Student, We know that componendo - divindo rules says that if \frac{a}{b} = \frac{c}{d} then it is also equal to \frac{a - c}{b - d} so here k = \frac{a^{2} + c^{2}}{a + c} = \frac{b^{2} + c^{2}}{b + c} = \frac{(a^{2} + c^{2}) - (b^{2} + c^{2})}{(a + c) - (b + c)} = \frac{a^{2} - b^{2}}{a - b} = \frac{(a + b) (a - b)}{a - b} = a + b so k = a + b Regards

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