1: ĐKXĐ: x<>0; y<>0
TA có: \(\begin{cases}\frac{15}{x}-\frac{7}{y}=9\\ \frac{4}{x}+\frac{8}{y}=-5\end{cases}\Rightarrow\begin{cases}\frac{60}{x}-\frac{28}{y}=36\\ \frac{60}{x}+\frac{120}{y}=-75\end{cases}\)
=>\(\begin{cases}\frac{60}{x}-\frac{28}{y}-\frac{60}{x}-\frac{120}{y}=36+75\\ \frac{4}{x}+\frac{8}{y}=-5\end{cases}\Rightarrow\begin{cases}\frac{-148}{y}=111\\ \frac{4}{x}+\frac{8}{y}=-5\end{cases}\)
=>\(\begin{cases}y=-\frac{148}{111}=-\frac43\\ \frac{4}{x}=-5-\frac{8}{y}=-5-8:\frac{-4}{3}=-5+8\cdot\frac34=-5+6=1\end{cases}\)
=>y=-4/3(nhận) và x=4(nhận)
2: ĐKXĐ: x<>y; x<>-y
\(\begin{cases}\frac{1}{x+y}+\frac{1}{x-y}=\frac58\\ \frac{1}{x+y}-\frac{1}{x-y}=-\frac38\end{cases}\Rightarrow\begin{cases}\frac{1}{x+y}+\frac{1}{x-y}+\frac{1}{x+y}-\frac{1}{x-y}=\frac58-\frac38\\ \frac{1}{x+y}-\frac{1}{x-y}=-\frac38\end{cases}\)
=>\(\begin{cases}\frac{2}{x+y}=\frac28\\ \frac{1}{x-y}=\frac{1}{x+y}+\frac38\end{cases}\Rightarrow\begin{cases}x+y=8\\ \frac{1}{x-y}=\frac18+\frac38=\frac48=\frac12\end{cases}\Rightarrow\begin{cases}x+y=8\\ x-y=2\end{cases}\)
=>\(\begin{cases}x=\frac{8+2}{2}=\frac{10}{2}=5\\ y=8-5=3\end{cases}\) (nhận)
4: ĐKXĐ: x<>0; y<>0
\(\begin{cases}\frac{3}{2x}+\frac{3}{2y}=1\\ \frac{1}{3x}+\frac{1}{4y}=\frac15\end{cases}\Rightarrow\begin{cases}\frac{1}{x}+\frac{1}{y}=\frac23\\ \frac13\cdot\frac{1}{x}+\frac14\cdot\frac{1}{y}=\frac15\end{cases}\)
=>\(\begin{cases}\frac13\cdot\frac{1}{x}+\frac13\cdot\frac{1}{y}=\frac29\\ \frac13\cdot\frac{1}{x}+\frac14\cdot\frac{1}{y}=\frac15\end{cases}\Rightarrow\begin{cases}\frac13\cdot\frac{1}{x}+\frac13\cdot\frac{1}{y}-\frac13\cdot\frac{1}{x}-\frac14\cdot\frac{1}{y}=\frac29-\frac15\\ \frac{1}{x}+\frac{1}{y}=\frac23\end{cases}\)
=>\(\begin{cases}\frac{1}{12}\cdot\frac{1}{y}=\frac{10-9}{45}=\frac{1}{45}\\ \frac{1}{x}+\frac{1}{y}=\frac23\end{cases}\Rightarrow\begin{cases}\frac{1}{y}=\frac{12}{45}=\frac{4}{15}\\ \frac{1}{x}=\frac23-\frac{4}{15}=\frac{10}{15}-\frac{4}{15}=\frac{6}{15}=\frac25\end{cases}\Rightarrow\begin{cases}y=\frac{15}{4}\\ x=\frac52\end{cases}\) (nhận)
5: ĐKXĐ: x>4
\(\begin{cases}\frac{2}{\sqrt{x-4}}-\left(y-1\right)=1\\ \frac{1}{\sqrt{x-4}}+2y-2=4\end{cases}\Rightarrow\begin{cases}\frac{2}{\sqrt{x-4}}-\left(y-1\right)=1\\ \frac{2}{\sqrt{x-4}}+4\left(y-1\right)=8\end{cases}\)
=>\(\frac{2}{\sqrt{x-4}}-\left(y-1\right)-\frac{2}{\sqrt{x-4}}-4\left(y-1\right)=1-8\)
=>-5(y-1)=-7
=>y-1=1,4
=>y=2,4
\(\frac{1}{\sqrt{x-4}}+2y-2=4\)
=>\(\frac{1}{\sqrt{x-4}}+2\cdot2,4-2=4\)
=>\(\frac{1}{\sqrt{x-4}}=4+2-4,8=6-4,8=1,2\)
=>\(\sqrt{x-4}=\frac56\)
=>x-4=25/36
=>x=25/36+4=25/36+144/36=169/36(nhận)
