[tex]Domain:\\4-x\neq0\ \wedge\ 4+x\neq0\\x\neq4\ \wedge\ x\neq-4\\\\\dfrac{4}{4-x}=\dfrac{5}{4+x}\qquad\text{cross multiply}\\\\4(4+x)=5(4-x)\qquad\text{use distributive property}\\\\(4)(4)+(4)(x)=(5)(4)+(5)(-x)\\\\16+4x=20-5x\qquad\text{subtract 16 from both sides}\\\\4x=4-5x\qquad\text{add 5x to both sides}\\\\9x=4\qquad\text{divide both sides by 9}\\\\\boxed{x=\dfrac{4}{9}}[/tex]
