a) Ta có:
\(\dfrac{A}{x-2}=\dfrac{x^2+3x+2}{x^2-4}\)
\(\Rightarrow A=\dfrac{\left(x-2\right)\left(x^2+3x+2\right)}{x^2-4}\)
\(\Rightarrow A=\dfrac{\left(x-2\right)\left(x^2+x+2x+2\right)}{x^2-2^2}\)
\(\Rightarrow A=\dfrac{\left(x-2\right)\left(x+1\right)\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}\)
\(\Rightarrow A=x+1\)
b) Ta có:
\(\dfrac{M}{x-1}=\dfrac{x^2+3x+2}{x+1}\)
\(\Rightarrow M=\dfrac{\left(x-1\right)\left(x^2+3x+2\right)}{x+1}\)
\(\Rightarrow M=\dfrac{\left(x-1\right)\left(x^2+x+2x+2\right)}{x+1}\)
\(\Rightarrow M=\dfrac{\left(x-1\right)\left(x+1\right)\left(x+2\right)}{x+1}\)
\(\Rightarrow M=\left(x-1\right)\left(x+2\right)\)
\(\Rightarrow M=x^2+2x-x-2\)
\(M=x^2+x-2\)
