a) \(7+2x=32-3x\)
\(\Leftrightarrow\) \(2x+3x=32-7\)
\(\Leftrightarrow\) \(5x=25\)
\(\Leftrightarrow\) \(x=5\)
b) \(\dfrac{x+4}{5}-x+4=\dfrac{x}{3}-\dfrac{x-2}{2}\)
\(\Leftrightarrow\) \(6\left(x+4\right)-30x+120=10x-15\left(x-2\right)\)
\(\Leftrightarrow\) \(6x+24-30x+120=10x-15x+30\)
\(\Leftrightarrow\) \(-24x+144=-5x+30\)
\(\Leftrightarrow\) \(-24x+5=30-144\)
\(\Leftrightarrow\) \(-19x=-144\)
\(\Leftrightarrow x=6\)
c) \(x^2+\left(x+3\right)\left(x+5\right)=9\)
\(\Leftrightarrow\) \(x^2+x^2-5x+3x-15=9\)
\(\Leftrightarrow\) \(2x^2-2x-15=9\)
\(\Leftrightarrow\) \(2x^2-2x-15-9=0\)
\(\Leftrightarrow\) \(2x^2-2x-24=0\)
\(\Leftrightarrow\) \(2x^2+6x-8x-24=0\)
\(\Leftrightarrow\) \(2x\left(x+3\right)-8\left(x+3\right)=0\)
\(\Leftrightarrow\) \(\left(x+3\right)\left(2x-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\2x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=4\end{matrix}\right.\)
d) \(\dfrac{x+2}{x-2}-\dfrac{3}{x+2}+\dfrac{3x+10}{4-x^2}=0\)
\(\Leftrightarrow\) \(\dfrac{x+2}{x-2}-\dfrac{3}{x+2}-\dfrac{3x+10}{\left(x-2\right)\left(x+2\right)}=0\) ĐKXD :\(x\text{≠ ± 2}\)
\(\Leftrightarrow\) \(\left(x+x^2\right)-3\left(x-2\right)-3x-10=0\)
\(\Leftrightarrow\) \(x^2+4x+4-3x+6-3x-10=0\)
\(\Leftrightarrow\) \(x^2-2x=0\)
\(\Leftrightarrow\) \(x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\end{matrix}\right.\left[{}\begin{matrix}x=0\\x=2\left(\text{loại}\right)\end{matrix}\right.\)
Phương trình có tập nghiệm \(S=\) {0}
