Монгол Бодлогын Сан

Заавар: $$a+\frac{b}{c}=\dfrac{ac+b}{c}$$ $$\dfrac{a:c}{b:c}=\dfrac{a}{b}$$

Бодолт: \begin{align*} 1&=\dfrac{1+\dfrac{2x-3}{x+2}}{2+\dfrac{3x-4}{2x+4}}+\dfrac{2+\dfrac{3x+2}{2x -1}}{3+\dfrac{5x+3}{2x-1}} & &\color{WildStrawberry}{\dfrac{{}\times(2x+4)}{{}\times(2x+4)}} & &\color{WildStrawberry}{\dfrac{{}\times(2x-1)}{{}\times(2x-1)}}\\ &=\dfrac{2x+4+2(2x-3)}{2(2x+4)+3x-4}+\dfrac{2(2x-1)+3x+2}{3(2x-1)+5x+3}\\ &=\dfrac{6x-2}{7x+4}+\dfrac{7x}{11x}=\dfrac{6x-2}{7x+4}+\dfrac{7}{11} \end{align*} тул $$\dfrac{6x-2}{7x+4}=\dfrac{4}{11}\Rightarrow 66x-22=28x+16\Rightarrow x=1$$ байна.