we have the expression
[tex]\frac{cd-c+d-1}{cd+c+d+1}[/tex]
Group terms
[tex]\frac{(cd+d)+(-c-1)}{(cd+d)+(c+1)}[/tex][tex]\frac{d(c+1)-(c+1)}{d(c+1)+(c+1)}[/tex]
factor (c+1)
[tex]\frac{(c+1)(d-1)}{(c+1)(d+1)}[/tex]
Simplify
[tex]\frac{(d-1)}{(d+1)}[/tex]
