Question

Solve the equation :-
1) 1/x - 1/x+ b = 1/a - 1/ a+b​

Answer 1

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Answer 2

Answer:

$\dfrac{1}{x} - \dfrac{1}{x + b} = \dfrac{1}{a} - \dfrac{1}{a + b}$

⇒ $\dfrac{x + b - x}{x(x + b)} =\: \dfrac{a + b - a}{a(a + b)}$

⇒ $\dfrac{b}{x(a + b)} =\: \dfrac{b}{a(x + b)}$

⇒ $\dfrac{1}{{x}^{2} + bx} =\: \dfrac{1}{{a}^{2} + ab}$

⇒ x² + bx = a² + ab

⇒x² - a² + bx - ab = 0

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

⇒( x - a )( x + a + b) = 0

⇒ x - a = 0 ; x + a + b = 0

⇒ x = a ; x = - (a + b)

➡ x = a, - (a + b)

∴ Then the required solution is x = a, - (a + b) .