Đáp án + Giải thích các bước giải:
$\left\{\begin{matrix}\dfrac{24}{x+5}-\dfrac{20}{x-y}=1& \\\dfrac{20}{x+5}-\dfrac{35}{x-y}=6& \end{matrix}\right.$ `(**)` `(ĐKXĐ:x\ne -5;x\ne y)`
Đặt `(4)/(x+5)=a\ (a\ne0);(5)/(x-y)=b\ (b\ne0)`
`(**)<=>` $\left\{\begin{matrix}6a-4b=1& \\5a-7b=6& \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}42a-28b=7& \\20a-28b=24& \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}22a=-17& \\5a-7b=6& \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}a=-\dfrac{17}{22} & \\7b=-\dfrac{217}{22}& \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}a=-\dfrac{17}{22} (TM)& \\b=-\dfrac{31}{22} (TM)& \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}\dfrac{4}{x+5}=-\dfrac{17}{22} & \\\dfrac{5}{x-y}=-\dfrac{31}{22} & \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}-17(x+5)=4.22 & \\-31(x-y)=5.22 & \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}-17x-85= 88 & \\-31x+31y=110 & \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}-17x= 173 & \\31y=110+31x & \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}x= -\dfrac{173}{17} & \\31y=-\dfrac{3493}{17} & \end{matrix}\right.$
`<=>` $\left\{\begin{matrix}x= -\dfrac{173}{17} (TM) & \\y=-\dfrac{3493}{527} (TM) & \end{matrix}\right.$
Vậy hệ phương trình có nghiệm là : `(x;y)=(-(173)/(17);-(3493)/(527))`
