$\frac{1}{P}+\frac{2}{Q}+\frac{3}{R}=$কত?

‘খ’ থেকে পাই,

$P = x^3 - 3x^2 - 10x = x(x - 5)(x + 2)$
$Q = x^3 + 6x^2 + 8x = x(x + 2)(x + 4)$
$R = x^2 - x - 20 = (x - 5)(x + 4)$

∴ $\frac{1}{P} + \frac{2}{Q} + \frac{3}{R}$

$$= \frac{1}{x(x - 5)(x + 2)} + \frac{2}{x(x + 2)(x + 4)} + \frac{3}{(x - 5)(x + 4)}$$

$$= \frac{1(x + 4) + 2(x - 5) + 3x(x + 2)}{x(x + 2)(x + 4)(x - 5)}$$

$$= \frac{x + 4 + 2x - 10 + 3x^2 + 6x}{x(x + 2)(x + 4)(x - 5)} = \frac{3x^2 + 9x - 6}{x(x + 2)(x + 4)(x - 5)}$$

নির্ণেয় মান: $$\frac{3x^2 + 9x - 6}{x(x + 2)(x + 4)(x - 5)}$$