Text Compute and simplify: x2−92x÷x−34x2.\frac{x^{2}-9}{2x}\div\frac{x-3}{4x^{2}}.2xx2−9÷4x2x−3. Solution Division becomes multiplication by the reciprocal: (x−3)(x+3)2x⋅4x2x−3=2x(x+3)=2x2+6x,x≠0, x≠3.\frac{(x-3)(x+3)}{2x}\cdot\frac{4x^{2}}{x-3}=2x(x+3)=2x^{2}+6x,\qquad x\neq 0,\ x\neq 3.2x(x−3)(x+3)⋅x−34x2=2x(x+3)=2x2+6x,x=0, x=3. 2x2+6x(x≠0, 3) \boxed{\,2x^{2}+6x\quad (x\neq 0,\,3)\,}2x2+6x(x=0,3)