Question

$frac{1}{x+ frac{1}{1+ frac{x+2}{x-2} } } = frac{12}{12x-7}$

Answer 1

$frac{1}{x+ frac{1}{1+ frac{x+2}{x-2} } } = frac{12}{12x-7}$

$12x-7 = {12}*({x+ frac{1}{1+ frac{x+2}{x-2} })$

$12x-7 = {12x}{+ frac{12}{1+ frac{x+2}{x-2} }$

$-7 = frac{12}{1+ frac{x+2}{x-2} }$

$-7 * ({1+ frac{x+2}{x-2} }) = {12}$

$frac{-7(x+2)}{x-2} } = {19}$

${-7(x+2)} = {19}(x-2)$

$-7x-14 = 19x-38$

$38-14 = 19x+7x$

$26x = 24$

$x = frac{12}{13}$

Answer 2

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