Giải các bất phương trình sau: a) $\frac{x - 2}{x - 3}$ > 0 b) $\frac{x + 2 }{x - 5}$ < 0 c) $\frac{x - 1}{x + 3}$ > 1
1 câu trả lời
Đáp án:
\(\begin{array}{l}
a)\left[ \begin{array}{l}
x > 3\\
x < 2
\end{array} \right.\\
b)5 > x > - 2\\
c)x < - 3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)DK:x \ne 3\\
\dfrac{{x - 2}}{{x - 3}} > 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 2 > 0\\
x - 3 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 2 < 0\\
x - 3 < 0
\end{array} \right.
\end{array} \right.\\
\to \left[ \begin{array}{l}
x > 3\\
x < 2
\end{array} \right.\\
b)DK:x \ne 5\\
\dfrac{{x + 2}}{{x - 5}} < 0\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x + 2 > 0\\
x - 5 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 2 < 0\\
x - 5 > 0
\end{array} \right.
\end{array} \right.\\
\to \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x > - 2\\
x < 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x < - 2\\
x > 5
\end{array} \right.\left( l \right)
\end{array} \right.\\
\to 5 > x > - 2\\
c)DK:x \ne - 3\\
\dfrac{{x - 1}}{{x + 3}} > 1\\
\to \dfrac{{x - 1 - x - 3}}{{x + 3}} > 0\\
\to \dfrac{{ - 4}}{{x + 3}} > 0\\
\to x + 3 < 0\\
\to x < - 3
\end{array}\)