Question 666617
Solve for x:

{{{(x-a)/(x-b) = (x-c)/(x-d)}}}

Cross multiply

{{{(x-a)(x-d) = (x-b)(x-c)}}}
{{{x^2-ax-dx +ad = x^2 -bx - cx + bc}}}
{{{-ax-dx+ad = -bx-cx+bc}}}
{{{-ax -dx +bx +cx = bc-ad}}}
{{{(-a-d+b+c)x = bc-ad}}}
{{{x = (bc-ad) /(b+c-a-d)}}}