Answer: b) x = -2, 4
Step-by-step explanation:
[tex]\dfrac{x+4}{4}=\dfrac{x}{x-2}\quad \rightarrow \quad \text{Restriction: }x\neq2\\\\\\\text{Cross Multiply:}\\(x+4)(x-2)=4x\\\\\\\text{Expand the left side:}\\x^2+2x-8=4x\\\\\\\text{Subtract 4x from both sides:}\\x^2-2x-8=0\\\\\\\text{Factor the quadratic equation:}\\(x+2)(x-4)=0\\\\\\\text{Apply the Zero Product Property and solve for x:}\\x+2=0\qquad x-4=0\\x=-2\qquad \quad x=4\\\\[/tex]
