Question

plss help me frnds it's urgent

Answer 1

X/X+1 + X+1/X = 61/30
(X²+X²+2X+1)/X²+X = 61/30
61X² + 61X = 60X² + 60X + 30
X² + X + 30 = 0
X² - 5X + 6X +30 = 0
X(X-5) + 6(X-5)

Therefore X= +5 or X= - 6

Answer 2

$\frac{x}{x + 1} + \frac{x + 1}{x} = \frac{61}{30 } \\ or. \: \frac{x}{x + 1} - 1 + \frac{x + 1}{x} - 1 = \frac{61}{30} - 2 \\ or. \frac{x - 1 - x}{x + 1} + \frac{x + 1 - x}{x} = \frac{1}{30} \\ or. \: - \frac{1}{x + 1} + \frac{1}{x} = \frac{1}{30} \\ or. \: \frac{ - x + x + 1}{x(x + 1)} = \frac{1}{30} \\ or. \: 30 = {x}^{2} + x \\ or. \: {x}^{2} + x - 30 = 0 \\ or. {x}^{2} + 6x - 5x - 30 = 0 \\ or. \: x(x + 6) - 5(x + 6) = 0 \\ or. \: (x - 5)(x + 6) = 0 \\ so \: \: either \: x = 5.......or \: \: \: x = - 6$
Hope x = 5, - 6 is ur required answer