a: Sửa đề: \(\dfrac{1}{x+2}+\dfrac{3}{x^2-4}+\dfrac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)
\(=\dfrac{1}{x+2}+\dfrac{3}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-14}{\left(x+2\right)^2\cdot\left(x-2\right)}\)
\(=\dfrac{x^2-4+3\left(x+2\right)+x-14}{\left(x+2\right)^2\cdot\left(x-2\right)}\)
\(=\dfrac{x^2+x-18+3x+6}{\left(x+2\right)^2\cdot\left(x-2\right)}\)
\(=\dfrac{x^2+4x-12}{\left(x+2\right)^2\cdot\left(x-2\right)}=\dfrac{\left(x+6\right)\left(x-2\right)}{\left(x+2\right)^2\cdot\left(x-2\right)}\)
\(=\dfrac{x+6}{\left(x+2\right)^2}\)
b: \(\dfrac{18}{\left(x-3\right)\left(x^2-9\right)}-\dfrac{3}{x^2-6x+9}-\dfrac{x}{x^2-9}\)
\(=\dfrac{18}{\left(x-3\right)^2\cdot\left(x+3\right)}-\dfrac{3}{\left(x-3\right)^2}-\dfrac{x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{18-3\left(x+3\right)+x\left(x-3\right)}{\left(x-3\right)^2\cdot\left(x+3\right)}\)
\(=\dfrac{18-3x-9+x^2-3x}{\left(x-3\right)^2\cdot\left(x+3\right)}\)
\(=\dfrac{x^2-6x+9}{\left(x-3\right)^2\cdot\left(x+3\right)}=\dfrac{1}{x+3}\)
