Question

solve and verify the following
x+b÷a-b=x-b÷a+b​

Answer 1

$\huge{\text{\underline{Question:-}}}$

x + b ÷ a - b = x - b ÷ a + b

$\huge{\text{\underline{Solution:-}}}$

★ Given:-

$\implies$x + b / a - b = x - b / a + b

★ Explaination:-

$\implies$(x + b)(a + b) = (x - b)(a - b)

$\implies{\tt{xa + xb + ab + b^2 = xa - bx - ba + b^2}}$

$\implies{\tt{xa + xb + ab + b^2 - xa + bx + ba - b^2}}$

$\implies$2xb + 2ab = 0

$\implies$2b (x + a) = 0

$\implies$x + a = 0

$\implies\large{\boxed{\text{x = - a}}}$

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Answer 2

SOLUTION:-

Given:

x+b÷ a -b= x-b÷a+b

To find:

Solve & verify.

Explanation:

$\frac{x + b}{a - b} = \frac{x - b}{a + b} \\ (cross \: multiplication) \\ \\ (a + b)(x + b) = (x - b)(a - b) \\ \\ a(x + b) + b(x + b) = x(a - b) - b(a - b) \\ \\ ax + ab + bx + {b}^{2} = ax - bx - ab + {b}^{2} \\ \\ ab + ab + bx + bx = 0 \\ \\ 2ab + 2bx = 0 \\ \\ 2b(a + x) = 0 \\ \\ a + x = \frac{0}{2b} \\ \\ a + x = 0 \\ \\ x = - a$

Hope it helps ☺️