a, \(A=\dfrac{x+2}{x+3}-\dfrac{5}{\left(x-2\right)\left(x+3\right)}\)
\(\Rightarrow A=\dfrac{\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}-\dfrac{5}{\left(x-2\right)\left(x+3\right)}\)
\(\Rightarrow A=\dfrac{x^2-4}{\left(x-2\right)\left(x+3\right)}-\dfrac{5}{\left(x-2\right)\left(x+3\right)}\)
\(\Rightarrow A=\dfrac{x^2-4-5}{\left(x-2\right)\left(x+3\right)}\)
\(\Rightarrow A=\dfrac{x^2-9}{\left(x-2\right)\left(x+3\right)}\)
\(\Rightarrow A=\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}\)
\(\Rightarrow A=\dfrac{x-3}{x-2}\)
\(b,\dfrac{x-3}{x-2}=5\\ \Rightarrow x-3=5x-10\\ \Rightarrow4x-7=0\\ \Rightarrow4x=7\\ \Rightarrow x=\dfrac{7}{4}\)
c,\(\dfrac{x-3}{x-2}=\dfrac{-2-3}{-2-4}=\dfrac{-5}{-6}=\dfrac{5}{6}\)
