\(\dfrac{x-1}{13}-\dfrac{2x-13}{15}=\dfrac{3x-15}{27}-\dfrac{4x-27}{29}\)
\(\Rightarrow\left(\dfrac{x-1}{13}-1\right)-\left(\dfrac{2x-13}{15}-1\right)=\left(\dfrac{3x-15}{27}-1\right)-\left(\dfrac{4x-27}{29}-1\right)\)
\(\Rightarrow\dfrac{x-14}{13}-\dfrac{2\left(x-14\right)}{15}=\dfrac{3\left(x-14\right)}{27}-\dfrac{4\left(x-14\right)}{29}\)
\(\Rightarrow\dfrac{x-14}{13}-\dfrac{2\left(x-14\right)}{15}-\dfrac{3\left(x-14\right)}{27}+\dfrac{4\left(x-14\right)}{29}=0\)
\(\Rightarrow\left(x-14\right)\left(\dfrac{1}{13}-\dfrac{2}{15}-\dfrac{3}{27}+\dfrac{4}{29}\right)=0\)
\(\Rightarrow x-14=0\) (vì \(\dfrac{1}{13}-\dfrac{2}{15}-\dfrac{3}{27}+\dfrac{4}{29}\ne0\))
\(\Rightarrow x=14\)
\(\dfrac{x-1}{13}-\dfrac{2x-13}{15}=\dfrac{3x-15}{27}-\dfrac{4x-27}{29}\)
=>\(\left(\dfrac{x-1}{13}-1\right)-\left(\dfrac{2x-13}{15}-1\right)=\left(\dfrac{3x-15}{27}-1\right)-\left(\dfrac{4x-27}{29}-1\right)\)
=>\(\dfrac{x-14}{13}-\dfrac{2x-28}{15}=\dfrac{3x-42}{27}-\dfrac{4x-56}{29}\)
=>\(\left(x-14\right)\left(\dfrac{1}{13}-\dfrac{2}{15}-\dfrac{3}{27}+\dfrac{4}{29}\right)=0\)
=>x-14=0
=>x=14
