Text Simplify, stating the conditions of existence: x2−16x2+8x+16.\frac{x^{2}-16}{x^{2}+8x+16}.x2+8x+16x2−16. Solution Factorise numerator and denominator: (x−4)(x+4)(x+4)2=x−4x+4,x≠−4.\frac{(x-4)(x+4)}{(x+4)^{2}}=\frac{x-4}{x+4},\qquad x\neq -4.(x+4)2(x−4)(x+4)=x+4x−4,x=−4. x−4x+4(x≠−4) \boxed{\,\dfrac{x-4}{x+4}\quad (x\neq-4)\,}x+4x−4(x=−4)