Question

determine no campo dos números inteiros, o conjunto verdade da equação :
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Answer 1

$\dfrac{x}{x+1}+\dfrac{x+1}{x}=\dfrac{13}{6}$

$\dfrac{x^2+(x+1)^2}{(x+1)x}=\dfrac{13}{6}$

$\dfrac{x^2+x^2+2x+1}{x^2+x}=\dfrac{13}{6}$

$6(2x^2+2x+1)=13(x^2+x)$

$12x^2+12x+6=13x^2+13x$

$\boxed{x^2+x-6=0}$

$a=1,\ b=1,\ c=-6$

$\boxed{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}$

$x=\dfrac{-1\pm\sqrt{1^2-4(1)(-6)}}{2(1)}=\dfrac{-1\pm5}{2}$

$\boxed{x=-3}\ \text{ou}\ \boxed{x=+2}$

$\boxed{\mathbb{S}=\{x\in\mathbb{Z}\ |\ x=-3\ \text{ou}\ x=2\}}$