Cách 1:
$\dfrac{36}{x+6}+\dfrac{36}{x-6}=4,5$
$⇔ \dfrac{36(x-6)+36(x+6)}{(x-6)(x+6)}=\dfrac{4,5(x-6)(x+6)}{(x-6)(x+6)}$
$⇔ \dfrac{36(x-6+x+6)}{(x-6)(x+6)}=\dfrac{4,5(x²-36)}{(x-6)(x+6)}$
$⇔ 4,5x²-72x-162=0$
$⇔ 4,5x²+9x-81x-162=0$
$⇔ 4,5x(x+2)-81(x+2)=0$
$⇔ (4,5x-81)(x+2)=0$
\(⇔\left[ \begin{array}{l}4,5x-81=0\\x+2=0\end{array} \right.\)
\(⇔\left[ \begin{array}{l}x=18\\x=-2\end{array} \right.\)
Cách 2:
$4,5x^2 - 72x - 162 = 0$
$Δ=(-72)²-4.4,5.(-162)$
$Δ=5184-(-2916)$
$Δ=8100$
Vì $Δ>0$ nên ta có 2 nghiệm phân biệt:
$x_1=\dfrac{72+\sqrt{8100}}{2.4,5}=\dfrac{162}{9}=18$
$x_2=\dfrac{72-\sqrt{8100}}{2.4,5}=\dfrac{-18}{9}=-2$
