Question

Solve for x with clear steps.

Answer 1

$\frac{x-2}{x-4}+\frac{x-6}{x-8}=6\frac{2}{3}\\\\\frac{x-2}{x-4}+\frac{x-6}{x-8}=\frac{20}{3}\\\\\frac{(x-2)(x-8)+(x-6)(x-4)}{(x-4)(x-8)}=\frac{20}{3}\\\\\frac{x^2-10x+16+x^2-10x+24}{x^2-12x+32}=\frac{20}{3}\\\\\frac{2x^2-20x+40}{x^2-12x+32}=\frac{20}{3}\\\\3(2x^2-20x+40)=20(x^2-12x+32)\\\\6x^2-60x+120=20x^2-240x+640\\\\14x^2-180x+520=0$

equation convert in 
                                7x² - 90x + 260 = 0
     find discriminant D = (90)² - 4 × 7 × 260 = 8100-7280= 820 ⇒  positive 
now use quadratic formula ,
          $x =\frac{-b\pm\sqrt{D}}{2a}$
so, x = { 90 +_√820}/14 

Answer 2

The required answer is in the attachment.