\(M=\dfrac{\left|x+1\right|+2x}{3x^2-2x-1}\)
a) ĐKXĐ : \(x\ne-\dfrac{1}{3};1\).
Rút gọn :
+) Khi \(x\ge-1\) :
\(M=\dfrac{x+1+2x}{\left(x+\dfrac{1}{3}\right)\cdot\left(x-1\right)}\)
\(\Leftrightarrow\dfrac{3x+1}{\left(x+\dfrac{1}{3}\right)\cdot\left(x-1\right)}\)
\(\Leftrightarrow\dfrac{3\cdot\left(x+\dfrac{1}{3}\right)}{\left(x+\dfrac{1}{3}\right)\cdot\left(x-1\right)}\)
\(\Leftrightarrow\dfrac{3}{x-1}\).
+) Khi \(x< -1\) :
\(M=\dfrac{-1-x+2x}{\left(x+\dfrac{1}{3}\right)\cdot\left(x-1\right)}\)
\(\Leftrightarrow\dfrac{x-1}{\left(x+\dfrac{1}{3}\right)\cdot\left(x-1\right)}\)
\(\Leftrightarrow\dfrac{1}{x+\dfrac{1}{3}}\)
b) pt \(4x^2+5x-9=0\) có hai nghiệm \(\left[{}\begin{matrix}x=1\left(KTMĐK\right)\\x=-\dfrac{9}{4}\left(TMĐK\right)\end{matrix}\right.\)
Mà \(-\dfrac{9}{4}< -1\).
=> Giá trị của M : \(M=\dfrac{1}{-\dfrac{9}{4}+\dfrac{1}{3}}=-\dfrac{12}{23}\)
