Answer : the solution of c is 14.
Explanation :
Since we have given that
[tex]\frac{c-4}{c-2}=\frac{c-2}{c+2}-\frac{1}{2-c}\\\\\frac{c-4}{c-2}=\frac{c-2}{c+2}+\frac{1}{c-2}\\\\\frac{c-4}{c-2}=\frac{(c-2)^2+c+2}{(c+2)(c-2)}\\\\\frac{c-4}{c-2}=\frac{c^2+4-4c+c+2}{(c+2)(c-2)}\\\\(c-4)(c+2)=c^2+6-3c\\\\c^2-8-2c=c^2+6-3c\\\\-2c+3c=6+8\\\\c=14[/tex]
So, c = 14
So, the solution of c is 14.
There is no extraneous solution as if we put the value of c i.e. 14 in the equation it does not make the equation not defined . so by putting the value of c we get a defined value,
Hence , there is no extraneous solution.
