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a)
\frac{5}{x}=\frac{x}{20}
100=x^2
10=x
b)
\frac{x}{6}=\frac{3}{2x}
2x^2=18
x^2=9
x=3
c)
\frac{x+1}{x+6}=\frac{1}{x}
x\left(x+1\right)=1\left(x+6\right)
x^2+x=x+6
x^2=x-x+6
x^2=6
x=\sqrt{6}