Answer:
After solving the equation [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex] we get x=-2 and x= 4 i.e {-2,4}.
Option B is correct.
Step-by-step explanation:
We need to solve [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex]
Solving:
[tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex]
Cross multiply
[tex](x-2)(x+4)=x*4[/tex]
Multiplying:
[tex]x(x+4)-2(x+4)=4x\\x^2+4x-2x-8=4x\\x^2+2x-8-4x=0\\x^2-2x-8=0[/tex]
Now, we have got quadratic equation [tex]x^2-2x-8=0[/tex]
Solving this quadratic equation using quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]
We have a=1, b=-2 and c=-8 Putting values
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-8)}}{2(1)}\\x=\frac{2\pm\sqrt{4+32}}{2}\\x=\frac{2\pm\sqrt{36}}{2}\\x=\frac{2\pm6}{2}\\x=\frac{2+6}{2} \ or \ x=\frac{2-6}{2}\\x=\frac{8}{2} \ or \ x=\frac{-4}{2}\\x=4 \ or \ x=-2[/tex]
So,after solving the equation [tex]\frac{x+4}{4}=\frac{x}{x-2}[/tex] we get x=-2 and x= 4 i.e {-2,4}.
Option B is correct.
