What is the answer to x squared minus 16 divided by x minus 4 plus x squared equals 16?

Your equation is not clear

I can understand it in two ways

(x2-16)/x-4+x2=16

x=-4.59486 x=-0.793499 x=4.38835

or

x2-(16/x)-4+x2=16

x=3.50466 x=-0.864641 x=-2.64002