Đáp án:
3) \(\left[ \begin{array}{l}
x = 4\\
x = - 6\\
x = 0\\
x = - 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
1)\dfrac{{{{\left( { - 5} \right)}^2}.7}}{{45}} + \dfrac{{{{\left( { - 5} \right)}^2}.11}}{{45}}\\
= \dfrac{{5.7}}{9} + \dfrac{{5.11}}{9} = \dfrac{{35 + 55}}{9} = \dfrac{{90}}{9} = 10\\
2)\dfrac{{3x + 1}}{5} = \dfrac{{2 - 2x}}{6}\\
\to 18x + 6 = 10 - 10x\\
\to 28x = 4\\
\to x = \dfrac{1}{7}\\
3)A = \dfrac{{2x - 3}}{{x + 1}} = \dfrac{{2\left( {x + 1} \right) - 5}}{{x + 1}}\\
= 2 - \dfrac{5}{{x + 1}}\\
A \in Z \Leftrightarrow \dfrac{5}{{x + 1}} \in Z\\
\Leftrightarrow x + 1 \in U\left( 5 \right)\\
\to \left[ \begin{array}{l}
x + 1 = 5\\
x + 1 = - 5\\
x + 1 = 1\\
x + 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
x = 4\\
x = - 6\\
x = 0\\
x = - 2
\end{array} \right.
\end{array}\)
