Question

(x+b)÷(a-b)=(x-b)÷(a+b). Then, find the value of x.

Answer 1

Answer:

x = -a

Step-by-step explanation:

(x+b) ÷ (a-b) = (x-b) ÷ (a+b)

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

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

=> ax+bx+ab+b^2 = ax-bx-ab+b^2

=> bx + bx = - ab - ab

=> 2bx = -2ab

=> x = -2ab/2b

=> x = -a

Answer 2

$\frac{x+b}{a-b}=\frac{x-b}{a+b}$$xa+xb+ab+b^2-(xa-xb-ab+b^2)=0$

$\frac{x+b}{a-b}*\frac{a+b}{a+b}=\frac{x-b}{a+b}*\frac{a-b}{a-b}$

$\frac{xa+xb+ab+b^2}{a^2-b^2} = \frac{xa-xb-ab+b^2}{a^2-b^2}$

$xa+xb+ab+b^2=\frac{xa-xb-ab+b^2}{a^2-b^2}*a^2-b^2$

$xa+xb+ab+b^2=xa-xb-ab+b^2$

$xa+xb+ab+b^2-(xa-xb-ab+b^2)=0$

$xa+xb+ab+b^2-xa+xb+ab-b^2=0$

$2xb+2ab=0$

$2(xb+ab)=0$

$xb+ab=0$

$xb=-ab$

$x=\frac{-ab}{b}$

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