[latex] \frac{1}{x+ \frac{1}{1+ \frac{x+2}{x-2} } } = \frac{12}{12x-7} [/latex]

[latex] \frac{1}{x+ \frac{1}{1+ \frac{x+2}{x-2} } } = \frac{12}{12x-7} [/latex] [latex]12x-7 = {12}*({x+ \frac{1}{1+ \frac{x+2}{x-2} })[/latex] [latex]12x-7 = {12x}{+ \frac{12}{1+ \frac{x+2}{x-2} }[/latex] [latex]-7 = \frac{12}{1+ \frac{x+2}{x-2} }[/latex] [latex]-7 * ({1+ \frac{x+2}{x-2} }) = {12}[/latex] [latex] \frac{-7(x+2)}{x-2} } = {19}[/latex] [latex]{-7(x+2)} = {19}(x-2)[/latex] [latex]-7x-14 = 19x-38[/latex] [latex]38-14 = 19x+7x[/latex] [latex]26x = 24[/latex] [latex]x = \frac{12}{13} [/latex]