Solve each of the following equation and also check your result in each case:

$\frac{5 x}{3}-\frac{x-1}{4}=\frac{x-3}{5}$

or $\frac{20 x-3 x+3}{12}=\frac{x-3}{5}$

or $\frac{17 x+3}{12}=\frac{x-3}{5}$

or $85 x+15=12 x-36$

or $73 x=-51$

or $x=\frac{-51}{73}$

Check :

L. H.S. $=\frac{5 \times \frac{-51}{73}}{3}-\frac{\frac{-51}{73}-1}{4}=\frac{-255}{219}-\frac{-124}{292}=\frac{-54}{73}$

R.H.S. $=\frac{\frac{-51}{73}-3}{5}=\frac{-54}{73}$

$\therefore$ L.H.S. $=$ R.H.S. for $x=\frac{-51}{73}$