જો frac{2x + 3}{(x + 1)(x - 3)} = frac{a}{x + | vedclass

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(B) આપેલ આંશિક અપૂર્ણાંક વિઘટન: $\frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3}$.બંને બાજુ $(x + 1)(x - 3)$ વડે ગુણતા: $2x + 3 = a(

Vedclass · Accepted Answer

$2$

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(B) આપેલ આંશિક અપૂર્ણાંક વિઘટન: $\frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3}$.બંને બાજુ $(x + 1)(x - 3)$ વડે ગુણતા: $2x + 3 = a(x - 3) + b(x + 1)$.$x = -1$ લેતા: $2(-1) + 3 = a(-1 - 3)$ $\Rightarrow 1 = -4a$ $\Rightarrow a = -\frac{1}{4}$.$x = 3$ લેતા: $2(3) + 3 = b(3 + 1)$ $\Rightarrow 9 = 4b$ $\Rightarrow b = \frac{9}{4}$.તેથી,$a + b = -\frac{1}{4} + \frac{9}{4} = \frac{8}{4} = 2$.

જો $\frac{2x + 3}{(x + 1)(x - 3)} = \frac{a}{x + 1} + \frac{b}{x - 3}$ હોય,તો $a + b$ ની કિંમત શોધો.

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