a: ĐKXĐ: x<>-2
\(\dfrac{x^2}{3x+6}+\dfrac{4x+4}{3x+6}\)
\(=\dfrac{x^2+4x+4}{3x+6}\)
\(=\dfrac{\left(x+2\right)^2}{3\left(x+2\right)}=\dfrac{x+2}{3}\)
b: ĐKXĐ: \(x\notin\left\{-2;-\dfrac{7}{4}\right\}\)
\(\dfrac{1}{x+2}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\)
\(=\dfrac{4x+7+1}{\left(x+2\right)\left(4x+7\right)}\)
\(=\dfrac{4x+8}{\left(x+2\right)\left(4x+7\right)}=\dfrac{4\left(x+2\right)}{\left(x+2\right)\left(4x+7\right)}=\dfrac{4}{4x+7}\)
c: ĐKXĐ: \(x\notin\left\{-2;2\right\}\)
\(\dfrac{3}{x+2}-\dfrac{2x}{x-2}+\dfrac{7}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{3\left(x-2\right)-2x\left(x+2\right)+7}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{3x-6-2x^2-4x+7}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{-2x^2-x+1}{\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{-2x^2-2x+x+1}{\left(x+2\right)\left(x-2\right)}=\dfrac{\left(x+1\right)\left(-2x+1\right)}{\left(x+2\right)\left(x-2\right)}\)
