First, let us express it into a mathematical equation:
[tex] \frac{6}{x} -6=( \frac{x}{x-6} )- \frac{6}{2} [/tex]
Then we simplify the equation by combining like terms
[tex] \frac{6}{2} -6=( \frac{x}{x-6} )- \frac{6}{x} [/tex]
[tex]-3 = \frac{ x^{2} -6(x-6)}{x(x-6)} [/tex]
[tex]-3 = \frac{ x^{2} -6x+36}{x(x-6)} [/tex]
[tex]-3 = \frac{ x^{2} -6x+36}{x(x-6)} [/tex]
[tex]-3x(x-6) = x^{2} -6x+36[/tex]
[tex]-3 x^{2} +18x = x^{2} -6x+36[/tex]
[tex]-3 x^{2} - x^{2} +6x-36+18x =0[/tex]
[tex]-4 x^{2} +24x-36 =0[/tex]
[tex](-4 x^{2} +24x-36 =0)/-4[/tex]
[tex]x^{2}-6x+9 =0[/tex]
[tex] (x-3)^{2} =0[/tex]
x = 3
There is a solution so it is not extraneous.
