Will give a solve and check : c-4/c-2=c-2/c+2 - 1/2-c the solution is c = how many extraneous solutions are there?

We have that
(c-4)/(c-2)=(c-2)/(c+2) - 1/(2-c)
 - 1/(2-c)=-1/-(c-2)=1/(c-2)

(c-4)/(c-2)=(c-2)/(c+2)+ 1/(c-2) > (c-4)/(c-2)-1/(c-2)=(c-2)/(c+2) 
(c-4-1)/(c-2)=(c-2)/(c+2) > (c-5)/(c-2)=(c-2)/(c+2)

(c-5)/(c-2)=(c-2)/(c+2) > remember (before simplifying) for the solution that c can not be 2 or -2
(c-5)*(c+2)=(c-2)*(c-2) > c²+2c-5c-10=c²-4c+4
-3c-10=-4c+4 > -3c+4c=4+10 > c=14

the solution is c=14
 
the domain of the function is (-∞,-2) U (-2,2) U (2,∞) or 
all real numbers except c=-2 and c=2