[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]