Question

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Answer 1

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$\frac{a - c}{(x - a)(a - b)} + \frac{b - c}{(b - a)(x - b)} \\ = \frac{(a - c)}{(x - a)(a - b)} - \frac{(b - c)}{(a - b)(x - b)} \\ = \frac{(a - c)(x - b) - (b - c)(x - a)}{(x - a)(x - b)(a - b) } \\ = \frac{ax - cx - ab + bc - xb + xc + ab - ac}{(a - b)(x - b)(x - a)} \\ = \frac{ax - bx - ac + bc}{(a - b)(x - a)(x - b)} \\ = \frac{x(a - b) - c(a - b)}{(x - a)(a - b)(x - b)} \\ = \frac{(x - c)(a - b)}{(a - b)(x - a)(x - b)} \\ = \frac{x - c}{(x - a)(x -b )}$
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