Find the value of $x$
$\frac{x+2}{2}- \frac{x+1}{5}=\frac{x-3}{4}-1$

Given: 

$\frac{x+2}{2}- \frac{x+1}{5}=\frac{x-3}{4}-1$

To find: The value of $x$

Solution:

$\frac{x+2}{2}- \frac{x+1}{5}=\frac{x-3}{4}-1$

Take LCM on both sides

$\frac{5(x+2)}{10}-\frac{2(x+1)}{10}$= $\frac{x-3-4}{4}$

$\frac{5x+10}{10}-\frac{2x+2}{10}=\frac{x-7}{4}$

$\frac{5x+10-2x-2}{10} = \frac{x-7}{4}$

$\frac{13x-2}{10}= \frac{x-7}{4}$

$4(13x-2)=10(x-7)$

$52x-8=10x-70$

$52x-10x=-70+8$

$42x=-62$

$x=\frac{-62}{40}$

$x=\frac{-31}{20}$

Therefore the value of $x=\frac{-31}{20}$