Question

Answer 1

\(\dfrac{2}{x\left(x+2\right)}=\dfrac{a}{x}+\dfrac{b}{x+2}\)

\(\Leftrightarrow\dfrac{2}{x\left(x+2\right)}=\dfrac{a\left(x+2\right)}{x\left(x+2\right)}+\dfrac{bx}{\left(x+2\right)x}\)

\(\Rightarrow ax+2a+bx=2\)

\(\Leftrightarrow\left(a+b\right)x+2a=2\)

\(\Leftrightarrow\left[{}\begin{matrix}a+b=0\\a=1\end{matrix}\right.\) (PP hệ số bất định)

\(\Leftrightarrow a=1;b=-1\)

-Giá trị của \(3a+2b=3.1-2.1=1\)