Step-by-step explanation:

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Verified answer

Answer:

We have been given:

[tex] \frac{x - a}{x - b} + \frac{x - b}{x - a} = \frac{a}{b} + \frac{b}{a} [/tex]

[tex] {x}^{2} + {a}^{2} - 2ax + {x}^{2} + {b}^{2} - 2bx = {a}^{2} + {b}^{2} [/tex]

2abx²-2(ab) (a+b)x + ab (a²+b²) = a²+b²x² - (a+b) (a²+b²)x + ab(a²+b²)

(a-b)²x² - (a+b) (a-b)²x=0

Therefore,

x(a-b) = 0

x = 0

or,

x-(a+b) = 0

x= a + b

Hence, x = 0 or x = a+b