Question

Solve the equation (x/x+2) - (4/x-2) = 1

Answer 1

Answer:

           $\bold{x=-\dfrac23}$

Step-by-step explanation:

$\dfrac x{x+2}-\dfrac4{x-2}=1\qquad\qquad\qquad x\ne2\ \wedge\ x\ne-2\\\\\\ \dfrac {x(x-2)}{(x+2)(x-2)}-\dfrac{4(x+2)}{(x-2)(x+2)}=1\\\\\\ \dfrac {x^2-2x-4x-8}{x^2-4}=1\\\\ \\\dfrac {x^2-6x-8}{x^2-4}=1\quad\iff\quad x^2-6x-8=x^2-4\\\\x^2-6x-8=x^2-4\\\\-6x-8=-4\\\\-6x=4\\\\x=-\frac46\\\\x=-\frac23$