Question

2x-6/x^3-3x^2-x+3 + Q=6/x-3 - 2x^2/1-x^2
Tính Q

Answer 1

\(\dfrac{2x-6}{x^3-3x^2-x+3}+Q=\dfrac{6}{x-3}+\dfrac{2x^2}{x^2-1}\)

\(\Rightarrow Q=\dfrac{6}{x-3}+\dfrac{2x^2}{\left(x-1\right)\left(x+1\right)}-\dfrac{2x-6}{\left(x-3\right)\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{6x^2-6+2x^3-6x^2-2x+6}{\left(x-3\right)\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{2x^3-2x}{\left(x-3\right)\left(x+1\right)\left(x-1\right)}=\dfrac{2x\left(x-1\right)\left(x+1\right)}{\left(x-3\right)\left(x+3\right)\left(x-1\right)}=\dfrac{2x}{x-3}\)