$\frac{x+1}{2009}$ + $\frac{x+3}{2007}$ = $\frac{x+5}{2005 }$ +$\frac{x+7}{1993}$
$\Rightarrow$ $1$ +$\frac{x+1}{2009}$ + $1$+ $\frac{x+3}{2007}$ = $1$ +$\frac{x+5}{2005 }$ +$1$+$\frac{x+7}{1993}$
$\Rightarrow$ $\frac{x+2000}{2009}$ + $\frac{x+2000 }{2007}$ = $\frac{x+2000}{2005 }$ +$\frac{x+2000}{1993}$
$\Rightarrow$ $\frac{x+2000}{2009}$ + $\frac{x+2000 }{2007}$ - $\frac{x+2000}{2005 }$ -$\frac{x+2000}{1993}$ =$0$
$\Rightarrow$( $x+2000$)$($ $\frac{1}{2009}$ + $\frac{1}{2007}$ - $\frac{1}{2005}$ - $\frac{1}{1993}$ $)$ = $0$
Vì ( $\frac{1}{2009}$ + $\frac{1}{2007}$ - $\frac{1}{2005}$ - $\frac{1}{1993}$ $)$ $\ne$ $0$
nên x+2000 =0 nên x=-2000
x) $\frac{392-x}{32}$ + $\frac{390-x}{34}$ + $\frac{388-x}{36}$ +$\frac{386-x}{38}$ + $\frac{384-x}{40}$ = $-5$
$\Rightarrow$ 1+ $\frac{392-x}{32}$ + 1+ $\frac{390-x}{34}$ + 1+ $\frac{388-x}{36}$ +1+$\frac{386-x}{38}$ +1+ $\frac{384-x}{40}$ = $-5$ + 1 + 1 + 1 + 1 + 1
$\Rightarrow$ $\frac{424 -x}{32}$ + $\frac{424-x}{34}$+ $\frac{424-x}{36}$ +$\frac{424-x}{38}$ + $\frac{424-x}{40}$ = $0$
$\Rightarrow$ $(424-x)$$($$\frac{1}{32}$ + $\frac{1}{34}$ + $\frac{1}{36}$ + $\frac{1}{38}$ + $\frac{1}{40}$$)$ = $0$
$Vì$ $($$\frac{1}{32}$ + $\frac{1}{34}$ + $\frac{1}{36}$ + $\frac{1}{38}$ + $\frac{1}{40}$$)$ $\ne$$0$
nên 424 - x = 0 nên x = 424
y)$\frac{x-15}{23}$ + $\frac{x-23}{15}$ -$2$ = $0$
$\Rightarrow$ $\frac{x-15}{23}$ + $\frac{x-23}{15}$ = $2$
$\Rightarrow$ $\frac{x-15}{23}$ - 1 +$\frac{x-23}{15}$-1 = $2$ -1-1
$\Rightarrow$ $\frac{x-38}{23}$ +$\frac{x-38}{15}$ = $0$
$\Rightarrow$ $(x-38)$$(\frac{1}{23}$ +$\frac{1}{15})$ = $0$
Vì $(\frac{1}{23}$ +$\frac{1}{15})$$\neq$ $0$
nên x- 38 = 0 nên x=38
