Đáp án: $x\in\{-1,3,\dfrac{11\pm\sqrt{55}}{11}\}$
Giải thích các bước giải:
$\left(\dfrac{x-1}{x}\right)^2+\left(\dfrac{x-1}{x-2}\right)^2=\dfrac{40}{9}$
$\to 9\left(x-1\right)^2\left(x-2\right)^2+9x^2\left(x-1\right)^2=40x^2\left(x-2\right)^2$
$\to 18x^4-72x^3+126x^2-108x+36=40x^4-160x^3+160x^2$
$\to -22x^4+88x^3-34x^2-108x+36=0$
$\to -2\left(x+1\right)\left(x-3\right)\left(11x^2-22x+6\right)=0$
$\to x\in\{-1,3,\dfrac{11\pm\sqrt{55}}{11}\}$
