Question

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

Answer 1

x+a/x-a=b-a/x-a
(x+a)(b+a)=(b-a)(x-a)
bx+ax+ab+a×a=bx-ax-ab+a×a
ax+ax+ab+ab=0
2ax+2ab=0
2a(x+b)=0
2a=0 or x+b=0
a=0 or x=-b

Answer 2

The given expression is:

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

We have to find, the value of x is:

Solution:

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

By cross-multiplication, we get

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

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

⇒ xb + xa + ab + $a^2$ = xb - xa - ab + $a^2$

⇒ xb - xb + xa + xa+ $a^2$  - $a^2$ = - ab - ab

⇒ xa + xa = - 2ab

⇒ 2xa = - 2ab

⇒ x = $\dfrac{- 2ab}{2a}$

⇒ x = - b

∴ x = - b

Thus, the value of 'x is equal to - b'.