Question

find the roots of the equation 1/x-1/x-2 =3, where (x≠0,2) by using formula ​

Answer 1

$\frac{1}{x} - \frac{1}{x - 2} = 3 \\ by \: taking \: lcm \: and \: cross \: multiplying \\ \: we \: get \\ = > \frac{(x - 2) - x}{(x)(x - 2)} = 3 \\ = > - 2 = 3(x)(x - 2) \\ = > - 2 = 3 {x}^{2} - 6x \\ = > 3 {x}^{2} - 6x + 2 = 0 \\ here \: we \: will \: use \: formula \: to \\ \: solve \: quadratic \: equation \: \\ = > x = \frac{ - b + | \sqrt{ {b}^{2} - 4ac } | }{2a} \\ = > x = \frac{ - ( -6) + | \sqrt{ {( - 6) }^{2} - 4(3)2} | }{2 \times 3} \\ = > x = \frac{6 + | \sqrt{36 - 24} | }{6} \\ = >x = \frac{6 + | \sqrt{12} | }{6} \\ = > x = \frac{ 6 + |2 \sqrt{3} |}{6 } \\ = > x = \frac{ 3 + \sqrt{3} }{3} .and \: \frac{3 - \sqrt{3} }{3} \\ hope \: it \: helps \: u \:$