Question

Xét dấu các biểu thức sau :

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

Answer 1

\(f\left(x\right)=\dfrac{3}{2x-1}-\dfrac{1}{x+2}=\dfrac{3\left(x+2\right)-\left(2x-1\right)}{\left(2x-1\right)\left(x+2\right)}\)
\(=\dfrac{x+7}{\left(2x-1\right)\left(x+2\right)}\).
\(x+7=0\Leftrightarrow x=-7\); \(2x-1=0\Leftrightarrow x=\dfrac{1}{2}\); \(x+2=0\Leftrightarrow x=-2\).

Vậy \(f\left(x\right)=0\) khi \(x=\left\{-7\right\}\).
\(f\left(x\right)>0\) khi \(x\in\left(-7;-2\right)\cup\left(\dfrac{1}{2};+\infty\right)\).
\(f\left(x\right)< 0\) khi \(\left(-\infty;-7\right)\cup\left(-2;\dfrac{1}{2}\right)\).
\(f\left(x\right)\) không xác định tại \(x=\left\{\dfrac{1}{2};-2\right\}\)