Question

Solve this question​

Answer 1

Answer:

a/x- b + b/x - a = 2

a( x-a) + b(x - b)/ (x-b)(x-a) = 2

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

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

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

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

3ax - a² + 3bx - b² = 2x² + 2ab

3ax - a² + 3bx - b² - 2x ² - 2ab = 0

3ax + 3bx - a² - b² - 2x² - 2ab = 0

use identy (a + b)²

2x² - 3x ( a + b)  + (a +b)²= 0

2x² - 2x( a + b) - x( a + b) + ( a + b )² = 0

2x [ x- ( a+ b ) - ( a + b) ] [( x - ( a+ b )] = 0

[ 2x - ( a + b) ] [ x - ( a + b) ] = 0

by zer property

2x = a + b , x = a + b

== x = a + b/2 ,  x =a + b

therefore value of x are

x = a + b/2 , x = a + b