Question

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

Answer 1

$\huge{ \mathfrak{answer}}$

( x -a)/(x -b) + ( x -b)/( x - a) =a/b + b/a

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

ab{ (x² -2a +a² + x² -2b +b²) = (a² + b²)(x² -ax -bx + ab)

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

(2ab -a² -b²)x² -(a +b)(2ab -a² -b²)x =0

(a² + b² -2ab)x² -(a +b)(a² +b² -2ab)x =0

(a -b)²x² -(a+b)(a-b)² x =0

x² -(a + b)x =0

x{ x -(a + b)} =0

x =0, (a + b)

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Answer 2

$\huge\red{\underline{{\boxed{\textbf{QUESTION}}}}}$

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

$\huge\red{\underline{{\boxed{\textbf{ANSWER}}}}}$

( x -a)/(x -b) + ( x -b)/( x - a) =a/b + b/a

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

ab{ (x² -2a +a² + x² -2b +b²) = (a² + b²)(x² -ax -bx + ab)

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

(2ab -a² -b²)x² -(a +b)(2ab -a² -b²)x =0

(a² + b² -2ab)x² -(a +b)(a² +b² -2ab)x =0

(a -b)²x² -(a+b)(a-b)² x =0

x² -(a + b)x =0

x{ x -(a + b)} =0

x =0, (a + b)

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HARSH PRATAP SINGH