frac{x + 1}{(x - 1)(x - 2)(x - 3)} ને આંશિક અ | vedclass

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Question

(C) ધારો કે $\frac{x + 1}{(x - 1)(x - 2)(x - 3)} = \frac{A}{x - 1} + \frac{B}{x - 2} + \frac{C}{x - 3}$.બંને બાજુ $(x - 1)(x - 2)(x - 3)$ વડે ગુણતા:$x

Vedclass · Accepted Answer

$\frac{1}{x - 1} - \frac{3}{x - 2} + \frac{2}{x - 3}$

Vedclass · Answer

(C) ધારો કે $\frac{x + 1}{(x - 1)(x - 2)(x - 3)} = \frac{A}{x - 1} + \frac{B}{x - 2} + \frac{C}{x - 3}$.બંને બાજુ $(x - 1)(x - 2)(x - 3)$ વડે ગુણતા:$x + 1 = A(x - 2)(x - 3) + B(x - 1)(x - 3) + C(x - 1)(x - 2)$.$x = 1$ માટે: $1 + 1 = A(1 - 2)(1 - 3) \implies 2 = 2A \implies A = 1$.$x = 2$ માટે: $2 + 1 = B(2 - 1)(2 - 3) \implies 3 = -B \implies B = -3$.$x = 3$ માટે: $3 + 1 = C(3 - 1)(3 - 2) \implies 4 = 2C \implies C = 2$.આમ,આંશિક અપૂર્ણાંક $\frac{1}{x - 1} - \frac{3}{x - 2} + \frac{2}{x - 3}$ છે.

$\frac{x + 1}{(x - 1)(x - 2)(x - 3)}$ ને આંશિક અપૂર્ણાંકમાં વિભાજિત કરો.

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