Ta có: \(A=\frac{1}{x\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+4\right)}+\cdots+\frac{1}{\left(x+18\right)\left(x+20\right)}\)
\(=\frac12\left(\frac{2}{x\left(x+2\right)}+\frac{2}{\left(x+2\right)\left(x+4\right)}+\cdots+\frac{2}{\left(x+18\right)\left(x+20\right)}\right)\)
\(=\frac12\left(\frac{1}{x}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+4}+\cdots+\frac{1}{x+18}-\frac{1}{x+20}\right)\)
\(=\frac12\left(\frac{1}{x}-\frac{1}{x+20}\right)=\frac12\cdot\frac{x+20-x}{x\left(x+20\right)}=\frac{20}{2x\left(x+20\right)}\)
\(=\frac{10}{x\left(x+20\right)}\)
=>Chọn B
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