\(a,A=2x^3+x^2-13x+6=2x^3-4x^2+5x^2-10x-3x+6\\ A=\left(x-2\right)\left(2x^2+5x-3\right)=\left(x-2\right)\left(2x^2+6x-x-3\right)\\ A=\left(x-2\right)\left(x+3\right)\left(2x-1\right)\\ \Rightarrow\dfrac{A}{2x^2+5x-3}=\dfrac{\left(x-2\right)\left(x+3\right)\left(2x-1\right)}{\left(2x-1\right)\left(x+3\right)}=x-2\\ \dfrac{A}{x^2+x-6}=\dfrac{\left(x-2\right)\left(x+3\right)\left(2x-1\right)}{\left(x-2\right)\left(x+3\right)}=2x-1\)
\(b,PT\left(1\right)=\dfrac{x}{\left(2x-1\right)\left(x+3\right)}=\dfrac{x\left(x-2\right)}{\left(2x-1\right)\left(x+3\right)\left(x-2\right)}\\ PT\left(2\right)=\dfrac{x+2}{\left(x-2\right)\left(x+3\right)}=\dfrac{\left(x+2\right)\left(2x-1\right)}{\left(2x-1\right)\left(x-2\right)\left(x+3\right)}\)
