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a: \(\left\{{}\begin{matrix}\dfrac{12}{x-3}-\dfrac{5}{y+2}=63\\\dfrac{8}{x-3}+\dfrac{15}{y+2}=-13\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{24}{x-3}-\dfrac{10}{y+2}=126\\\dfrac{24}{x-3}+\dfrac{45}{y+2}=-39\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{-55}{y+2}=165\\\dfrac{12}{x-3}-\dfrac{5}{y+2}=63\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y+2=\dfrac{-1}{3}\\\dfrac{12}{x-3}=48\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{7}{3}\\x=\dfrac{13}{4}\end{matrix}\right.\)
\(a,ĐK:x,y\ne2\)
Đặt \(\left\{{}\begin{matrix}x-2=a\\y-2=b\end{matrix}\right.\)
\(HPT\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{a}+\dfrac{3}{b}=5\\\dfrac{3}{a}+\dfrac{2}{b}=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{6}{a}+\dfrac{9}{b}=15\\\dfrac{6}{a}+\dfrac{4}{b}=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{a}+\dfrac{3}{b}=5\\\dfrac{5}{b}=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{a}+3=5\\b=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=1\end{matrix}\right.\Leftrightarrow x=y=3\left(tm\right)\)
\(b,ĐK:x\ge3;y\ge1\)
Sửa: \(\sqrt{x-3}-\sqrt{y-1}=4\)
Đặt \(\left\{{}\begin{matrix}a=\sqrt{x-3}\ge0\\b=\sqrt{y-1}\ge0\end{matrix}\right.\)
\(HPT\Leftrightarrow\left\{{}\begin{matrix}a-2b=2\\a-b=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a-b=4\\-b=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=6\\b=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x-3=36\\y-1=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=39\\y=5\end{matrix}\right.\)