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\left(2^{y}+1\right)x=2^{y}
Combine all terms containing x.
\frac{\left(2^{y}+1\right)x}{2^{y}+1}=\frac{2^{y}}{2^{y}+1}
Divide both sides by 2^{y}+1.
x=\frac{2^{y}}{2^{y}+1}
Dividing by 2^{y}+1 undoes the multiplication by 2^{y}+1.