Ta có:
\(VT=\dfrac{3}{31}+\left(\dfrac{1}{6}+\dfrac{-5}{9}\right):\left(\dfrac{7}{24}-\dfrac{13}{18}\right)\\ =\dfrac{3}{31}+\left(\dfrac{3}{18}+\dfrac{-10}{18}\right):\left(\dfrac{21}{72}-\dfrac{52}{72}\right)\\ =\dfrac{3}{31}+\dfrac{-7}{18}:\dfrac{-31}{72}\\ =\dfrac{3}{31}+\dfrac{28}{31}\\ =\dfrac{31}{31}=1\\ =2^{12}:2^{12}\\ =\left(2^3\right)^4:2^{12}=VP\)
\(VT=\dfrac{3}{31}+\left(\dfrac{1}{6}-\dfrac{5}{9}\right):\left(\dfrac{7}{24}-\dfrac{13}{18}\right)=\dfrac{3}{31}+\left(\dfrac{-21}{54}\right):\left(\dfrac{7}{24}-\dfrac{13}{18}\right)\)
\(=\dfrac{3}{31}+\left(-\dfrac{7}{18}\right):\left(\dfrac{7}{24}-\dfrac{13}{18}\right)=\dfrac{3}{31}-\dfrac{7}{18}:\left(\dfrac{7}{24}-\dfrac{13}{18}\right)=\dfrac{3}{31}+\dfrac{28}{31}=1=VP\)
Vậy ta có đpcm
