Question

solve the equation .....

Answer 1

$\underline\bold{\huge{ANSWER \: :}}$

$\frac{1}{x} - \frac{1}{x - b} = \frac{1}{a} - \frac{1}{a - b}$

=> $\frac{x - b - x}{x(x - b)} = \frac{a - b - a}{a(a - b)}$

=> $\frac{ - b}{x(x - b)} = \frac{ - b}{a(a - b)}$

=> $\frac{1}{ {x}^{2} - \: bx } = \frac{1}{ {a}^{2} - \: ab }$

=> a² - ab = x² - bx

=> a² - x² - ab + bx = 0

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

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

______________________________

$\bold{\huge{ULTIMATELY}}$

$\bold{EITHER}$

a + x - b = 0

=> x = (b - a)

______________________________

$\bold{OR}$

a - x = 0

=> a = x

Answer 2

1/x+1/a??