Giúp với ạ,cảm ơn rấtt nhìuuu

Đáp án:

$\dfrac{-13}{9}$

Giải thích các bước giải:

Đặt $A=0,(3)=0,3333...$

$\Rightarrow 10A=3,3333...\\\Rightarrow 10A-A=3,3333...-0,3333...\\\Rightarrow 9A=3\\\Rightarrow A=\dfrac13\\1\dfrac5{13}-\dfrac13-\left(1\dfrac49+\dfrac{18}{13}-\dfrac13\right)\\=\dfrac{18}{13}-\dfrac13-\dfrac{13}{9}-\dfrac{18}{13}+\dfrac13\\=\dfrac{18}{13}+\dfrac{-1}{3}+\dfrac{-13}{9}+\dfrac{-18}{13}+\dfrac13\\=\dfrac{18}{13}+\dfrac{-18}{13}+\dfrac{-1}3+\dfrac13+\dfrac{-13}{9}\\=\dfrac{-13}9$