If frac{(x - a)(x - b)}{(x - c)(x - d)} = fra | vedclass

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(D) Given the equation: $\frac{(x - a)(x - d)}{(x - c)(x - d)} = \frac{A}{x - c} - \frac{B}{x - d} + C$Multiply both sides by $(x - c)(x - d)$:$(x - a

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$1$

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(D) Given the equation: $\frac{(x - a)(x - d)}{(x - c)(x - d)} = \frac{A}{x - c} - \frac{B}{x - d} + C$Multiply both sides by $(x - c)(x - d)$:$(x - a)(x - b) = A(x - d) - B(x - c) + C(x - c)(x - d)$Expanding the right side:$x^2 - (a + b)x + ab = Ax - Ad - Bx + Bc + C(x^2 - (c + d)x + cd)$Equating the coefficients of $x^2$ on both sides:$1 = C$Therefore,$C = 1$.

If $\frac{(x - a)(x - b)}{(x - c)(x - d)} = \frac{A}{x - c} - \frac{B}{x - d} + C$,then $C =$

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