Question

x/x+1 + x+1/x=2*1/12, x≠0, -1
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Answer 1

Answer:

........................

Answer 2

Answer:

x = -4, 3

Step-by-step explanation:

$\frac{ {x }^{2} + (x + {1}^{2})}{x(x + 1)} = \frac{25}{12}$

$\frac{{x}^{2}+{x}^{2}+2.x.1+ {1}^{2}}{{x}^{2}+x } = \frac{25}{12}$

$\frac{ {x }^{2} + {x}^{2} + 2x + 1 }{ {x}^{2} + x = \frac{25}{12} } = \frac{25}{12}$

$\frac{ {2x}^{2} + 2x + 1}{ {x}^{2} + x } = \frac{25}{12}$

${24}^{2} + 24x + 12 = {25x}^{2} + 25x$

${24x}^{2} - {25x}^{2} + 24x - 25x + 12 = 0$

$- {x}^{2} - x + 12 = 0$

${x}^{2} + x - 12 = 0$

${x}^{2} + (4 - 3)x - 12 = 0$

${x}^{2} + 4x - 3x - 12 = 0$

$x(x + 4) - 3(x + 4) = 0$

$(x + 4)(x - 3) = 0$

is,

$(x + 4) = 0 \\ x = - 4$

or,

$(x - 3) = 0 \\ x = 3$