Question

How to solve (1/x+2)-(1/x-2)=1

Answer 1

$\large{\underline{\boxed{\text{Question:}}}} </p><p>$

$\frac{1}{x + 2} - \left (\frac{1}{x - 2} \right)= 1$

$\large{\underline{\boxed{\text{Solution:}}}}</p><p>$

We have,

$\frac{1}{x + 2} - \frac{1}{x - 2} = 1$

Simplifying by taking LCM

$\implies \frac{1(x - 2) - 1(x + 2)}{(x - 2)(x + 2)} = 1 \\ \\ \implies \frac{x - 2 - (x + 2)}{ {x}^{2} - {(2)}^{2} } = 1 \\ \\ \textsf{using identity} \\ \\ \underline { (a + b)(a - b) = {a}^{2} - {b}^{2} } \\ \\ \implies \frac{ \cancel {x} - 2 - \cancel {x} - 2}{ {x}^{2} - 4 } = 1 \\ \\ \implies - 4 = 1( {x}^{2} - 4) \\ \\ \implies {x}^{2} - 4 = - 4 \\ \\ \implies {x}^{2} = - \cancel{4} + \cancel{ 4}\\ \\ \implies {x}^{2} = 0 \\ \\ \implies \underline{\boxed{ \textsf{{\green{x = 0}}}}}$