x−bx−a+x−ax−b=

x−bx−a+x−ax−b(x−a)(x−b)(x−a)2+(x−b)2x2−(a+b)x+abx2−2ax−a2+x2−2bx−b2x2−(a+b)x+ab2x2−2(a+b)x−(a2+b2)

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{x-a}{x-b}+{x-b}{x-a}=

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

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\frac{x - a}{x - b} + \frac{x - b}{x - a} =

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\frac{x - a}{x - b} + \frac{x - b}{x - a} \frac{( x - a ) ^{2} + ( x - b ) ^{2}}{( x - a ) ( x - b )} \frac{x ^{2} - 2 a x - a ^{2} + x ^{2} - 2 b x - b ^{2}}{x ^{2} - ( a + b ) x + ab} \frac{2 x ^{2} - 2 ( a + b ) x - ( a ^{2} + b ^{2} )}{x ^{2} - ( a + b ) x + ab}

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