Question

Solve x+4/4 = x/x-2

Answer 1

Answer:

After solving the equation $\frac{x+4}{4}=\frac{x}{x-2}$ we get x=-2 and x= 4 i.e {-2,4}.

Option B is correct.

Step-by-step explanation:

We need to solve $\frac{x+4}{4}=\frac{x}{x-2}$

Solving:

$\frac{x+4}{4}=\frac{x}{x-2}$

Cross multiply

$(x-2)(x+4)=x*4$

Multiplying:

$x(x+4)-2(x+4)=4x\\x^2+4x-2x-8=4x\\x^2+2x-8-4x=0\\x^2-2x-8=0$

Now, we have got quadratic equation $x^2-2x-8=0$

Solving this quadratic equation using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

We have a=1, b=-2 and c=-8 Putting values

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-8)}}{2(1)}\\x=\frac{2\pm\sqrt{4+32}}{2}\\x=\frac{2\pm\sqrt{36}}{2}\\x=\frac{2\pm6}{2}\\x=\frac{2+6}{2} \ or \ x=\frac{2-6}{2}\\x=\frac{8}{2} \ or \ x=\frac{-4}{2}\\x=4 \ or \ x=-2$

So,after solving the equation $\frac{x+4}{4}=\frac{x}{x-2}$ we get x=-2 and x= 4 i.e {-2,4}.

Option B is correct.