Đặt \(\dfrac{x}{3}=\dfrac{y}{5}=k\left(k\ne0\right)\Rightarrow x=3k;y=5k\)
\(A=\dfrac{5x^2+3y^2}{5x^2-y^2}\\ A=\dfrac{5\cdot\left(3k\right)^2+3\cdot\left(5k\right)^2}{5\cdot\left(3k\right)^2-\left(5k\right)^2}\\ A=\dfrac{45k^2+75k^2}{45k^2-25k^2}\\ A=\dfrac{120k^2}{20k^2}=6\)
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Đặt \(\dfrac{x}{3}=\dfrac{y}{5}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3k\\y=5k\end{matrix}\right.\)
Ta có: \(A=\dfrac{5x^2+3y^2}{5x^2-y^2}\)
\(=\dfrac{5\cdot\left(3k\right)^2+3\cdot\left(5k\right)^2}{5\cdot\left(3k\right)^2-\left(5k\right)^2}\)
\(=\dfrac{5\cdot9k^2+3\cdot25k^2}{5\cdot9k^2-25k^2}\)
\(=\dfrac{45k^2+75k^2}{45k^2-25k^2}=\dfrac{120k^2}{20k^2}=6\)
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