Answer: x = -2/3
[tex]\frac{x}{x+2}- \frac{4}{x-2}=1\\\\<=>\frac{x(x-2)}{(x+2)(x-2)}-\frac{4(x+2)}{(x+2)(x-2)}=1\\\\\\<=>\frac{x(x-2)-4(x+2)}{(x-2)(x+2)}=1\\\\\\=>x(x-2)-4(x+2)=(x-2)(x+2)\\\\\\<=> x^{2} -2x-4x-8=x^{2} -4\\\\\\<=>-6x-8=-4\\\\\\<=>-6x=8-4\\\\\\<=>-6x=4\\\\\\<=>x=-4/6=-2/3[/tex]
Step-by-step explanation:
