$$\frac{123}{130}+x=\frac{-40}{41}+\frac{123}{130}$$
$x=-\frac{40}{41}\approx -0.975609756$
$$\frac{123}{130}+x=-\frac{40}{41}+\frac{123}{130}$$
$$\frac{123}{130}+x=-\frac{5200}{5330}+\frac{5043}{5330}$$
$$\frac{123}{130}+x=\frac{-5200+5043}{5330}$$
$$\frac{123}{130}+x=-\frac{157}{5330}$$
$$x=-\frac{157}{5330}-\frac{123}{130}$$
$$x=-\frac{157}{5330}-\frac{5043}{5330}$$
$$x=\frac{-157-5043}{5330}$$
$$x=\frac{-5200}{5330}$$
$$x=-\frac{40}{41}$$
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