Question

Solve the quadratic equation
$\frac{1}{x+1}+\frac{2}{x+2}=\frac{4}{x+4}$

Answer 1

$\frac{1}{x+1}+\frac{2}{x+2}=\frac{4}{x+4}$

$\frac{(x+2)+2(x+1)}{(x+1)(X+2)}=\frac{4}{x+4}$

$3x^2+16x+16=4x^2+12x8$

$x^2-4x-8=0$

$x=\frac{+4\pm \sqrt{16+32}}{2}=\frac{4\pm \sqrt{48}}{2}$

$x=2\pm 2\sqrt{3}$