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