Question

Tìm a, b để \(\frac{a}{x}+\frac{b}{1-x}=\frac{1}{x\left(1-x\right)}\)

Answer 1

\(\dfrac{a}{x}+\dfrac{b}{1-x}=\dfrac{a\left(1-x\right)}{x\left(1-x\right)}+\dfrac{b.x}{x\left(1-x\right)}=\dfrac{a-a.x+bx}{x\left(1-x\right)}=\dfrac{\left(b-a\right)x+a}{x\left(1-x\right)}\)

Để \(\dfrac{a}{x}+\dfrac{b}{1-x}=\dfrac{1}{x\left(1-x\right)}\) khi và chỉ khi \(\left\{{}\begin{matrix}b-a=0\\a=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=1\\b=1\end{matrix}\right.\)