Question

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

Answer 1

$a \div x - b \: \: \: \: + \: \: b \div x - a \: \: = 2$
{a(x-a) +b(x-b)} /(x-a) (x-b) =2

Answer 2

Answer:

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

Step-by-step explanation:

Given equation,

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

Take L.C.M of (x-b) and (x-a)

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

(a x - a² + b x - b²)/(x-a) (x-b) = 2

(a x - a² + b x - b²) = 2 (x-a) (x-b)

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

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

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

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