Question

Solve for $x:\frac{x-2}{x-4}+\frac{x-6}{x-8}=6\frac{2}{3}$

Answer 1

$\frac{x-2}{x-4}+\frac{x-6}{x-8}=\frac{20}{3}$

$3(x-2)(x-8)+3(x-6)(x-4)=20(x-4)(x-8)$

$3x^2-30x+48+3x^2-30x+72=20x^2-240x+640$

$6x^2-60x+120=20x^2-240x+640$

$-14x^2+180x-520=0$

$x=\frac{-180\pm \sqrt{{180}^2-4(-14)(-520)}}{2(-14)}$

$x=\frac{45\pm \sqrt{205}}{7}$