Question

solve
x-a/x-b+x-b/x-a=a²+b²/ab
( no unnecessary answers )​

Answer 1

Answer:

Step-by-step explanation:

x-a/x-b + x-b/x-a   = a² + b²/ab

=> (x-a)² + (x-b)² / (x-a)(x-b) = a² + b²/ab

=> x² - 2ax + a² + x² - 2bx + b² / x² - x(a+b) + ab =  a² + b²/ab

=> 2x² - 2x(a+b) + a² + b² / x² - x(a+b) + ab = a² + b²/ab

=> ab(2x² - 2x(a+b) + a² + b²) = (a² + b²) (x² - x(a+b) + ab)

=> 2abx² - 2ab(a+b)x + ab(a²+b²) = x²(a² + b²) - (a+b)(a²+b²)x + ab(a²+b²)          

=> - 2ab(a+b)x + (a+b)(a²+b²)x = x²(a² + b² -2ab)  (∵ab(a²+b²) is striked out)

=> (a+b)x( a²+b² -2ab) = x²(a² + b² -2ab)

=> x(a+b)(a-b)² = x²(a-b)²     (∵ (a-b)² is striked out)

=> x² -x(a+b) = 0

=> x(x - (a+b)) = 0

=> x = 0 or x - (a+b) = 0

=> x = 0 or x = a+b

Answer 2

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

x = 0 or (a+b)