a:
ĐKXĐ: \(x\notin\left\{2020;-2022\right\}\)
\(\dfrac{39x+7}{x-2020}\cdot\dfrac{9x-20}{x+2022}-\dfrac{39x+7}{x-2020}\cdot\dfrac{8x-2042}{x+2022}\)
\(=\dfrac{39x+7}{x-2020}\left(\dfrac{9x-20}{x+2022}-\dfrac{8x-2042}{x+2022}\right)\)
\(=\dfrac{39x+7}{x-2020}\cdot\dfrac{9x-20-8x+2042}{x+2022}\)
\(=\dfrac{39x+7}{x-2020}\cdot\dfrac{x+2022}{x+2022}=\dfrac{39x+7}{x-2020}\)
b: ĐKXĐ: \(x\notin\left\{9;-9\right\}\)
\(\dfrac{x^2-81}{x^2+101}\cdot\left(\dfrac{x^2+101}{x-9}+\dfrac{x^2+101}{x+9}\right)\)
\(=\dfrac{\left(x-9\right)\left(x+9\right)}{\left(x^2+101\right)}\cdot\left[\left(x^2+101\right)\cdot\left(\dfrac{1}{x-9}+\dfrac{1}{x+9}\right)\right]\)
\(=\dfrac{\left(x-9\right)\left(x+9\right)\left(x^2+101\right)}{\left(x^2+101\right)}\cdot\left(\dfrac{1}{x-9}+\dfrac{1}{x+9}\right)\)
\(=\left(x-9\right)\left(x+9\right)\cdot\dfrac{x+9+x-9}{\left(x+9\right)\left(x-9\right)}\)
=2x
c: ĐKXĐ: \(x\notin\left\{-100;-2\right\}\)
\(\dfrac{x^2-1}{x+100}\cdot\dfrac{2x}{x+2}+\dfrac{1-x^2}{x+100}\cdot\dfrac{x-100}{x+2}\)
\(=\dfrac{x^2-1}{x+100}\cdot\dfrac{2x}{x+2}-\dfrac{x^2-1}{x+100}\cdot\dfrac{x-100}{x+2}\)
\(=\dfrac{x^2-1}{x+100}\cdot\left(\dfrac{2x}{x+2}-\dfrac{x-100}{x+2}\right)\)
\(=\dfrac{x^2-1}{x+100}\cdot\dfrac{2x-x+100}{x+2}\)
\(=\dfrac{x^2-1}{x+2}\)
