X-a/x-b + x-b/x-a =a/b + b/a …

${{x - a} \over {x - b}} + {{x - b} \over {x - a}} = {a \over b} + {b \over a}$

=>     ${{{x^2} + {a^2} - 2ax + {x^2} + {b^2} - 2bx} \over {{x^2} - ax - bx + ab}} = {{{a^2} + {b^2}} \over {ab}}$

=>     ${{2{x^2} + {a^2} - 2ax + {b^2} - 2bx} \over {{x^2} - ax - bx + ab}} = {{{a^2} + {b^2}} \over {ab}}$

=>     $2ab{x^2} + {a^3}b - 2{a^2}bx + a{b^3} - 2a{b^2}x = {a^2}{x^2} - {a^3}x - {a^2}bx + {a^3}b + {b^2}{x^2} - a{b^2}x - {b^3}x + a{b^3}$

=>     $2ab{x^2} - {a^2}bx - a{b^2}x = {a^2}{x^2} - {a^3}x + {b^2}{x^2} - {b^3}x$

=>     ${a^2}{x^2} - 2ab{x^2} + {b^2}{x^2} - {a^3}x - {b^3}x + {a^2}bx + a{b^2}x = 0$

=>     ${x^2}\left( {{a^2} + {b^2} - 2ab} \right)+x\left( { - {a^3} - {b^3} + {a^2}b + a{b^2}} \right) = 0$

=>     $x\left[ {x\left( {{a^2} + {b^2} - 2ab} \right) + \left( { - {a^3} - {b^3} + {a^2}b + a{b^2}} \right)} \right] = 0$

=>     $x = 0$ Or $x = {{{a^3} + {b^3} - {a^2}b - a{b^2}} \over {{{\left( {a - b} \right)}^2}}}$

x - a /x - b + x - b / x - a = a/b + b/a

x2 + a2 - 2ax + x2 + b2 - 2bx /x2 + ab -ax - bx = a2 + b2 /ab