Đặt \(\frac{x}{3}=\frac{y}{5}=k\left(k≠0\right)\Rightarrow\hept{\begin{cases}x=3k\\y=5k\end{cases}}\Rightarrow A=\frac{5\left(3k\right)^2+3\left(5k\right)^2}{10\left(3k\right)^2-3\left(5k\right)^2}\)

\(\Rightarrow A=\frac{45k^2+75k^2}{90k^2-75k^2}=\frac{120k^2}{15k^2}=8\left(\text{do k ≠ 0}\right)\)

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Đặt \(\frac{x}{3}=\frac{y}{5}=n\Rightarrow x=3n;y=5n\)

\(\Rightarrow A=\frac{5.3^2n^2+3.5^2n^2}{10.3^2n^2-3.5^2n^2}=\frac{n^2\left(45+75\right)}{n^2\left(90-75\right)}=\frac{n^2.120}{n^2.25}=\frac{24}{5}\)

\(\frac{x}{3}=\frac{y}{5}\Rightarrow5x=3y\)

Thay 3y = 5x ; ta được: 

\(A=\frac{5x^2+5x^2}{10x^2-5x^2}=\frac{2\times5x^2}{2\times5x^2-5x^2}=\frac{2\times5x^2}{5x^2\times\left(2-1\right)}=\frac{2\times5x^2}{5x^2\times1}=2\)  

Đặt \(\frac{x}{3}=\frac{y}{5}=k\Rightarrow x=3k;y=5k\)

\(A=\frac{5x^2+3y^2}{10x^2-3y^2}=\frac{5.\left(3k\right)^2+3.\left(5k\right)^2}{10.\left(3k\right)^2-3.\left(5k\right)^2}=\frac{5.3^2.k^2+3.5^2.k^2}{10.3^2.k^2-3.5^2.k^2}\)

\(A=\frac{45k^2+75k^2}{90k^2-75k^2}=\frac{\left(45+75\right).k^2}{\left(90-75\right).k^2}=\frac{120k^2}{15k^2}=\frac{120}{15}=8\)

Vậy A=8
 

Đặt \(\frac{x}{3}=\frac{y}{5}=k\Rightarrow x=3k;y=5k\) Thay vào P ta được :

\(P=\frac{5.\left(3k\right)^2+3.\left(5k\right)^2}{10.\left(3k\right)^2-3\left(5k\right)^2}=\frac{45k^2+75k^2}{90k^2-75k^2}=\frac{15k^2\left(3+5\right)}{15k^2\left(6-5\right)}=\frac{3+5}{6-5}=\frac{8}{1}=8\)

Vậy \(P=8\)

ta có: x/3=y/5 suy ra x^2 /9=y^2/25

A[s dụng tính chất dãy tỉ số bằng nhau ta có: 

x^2/9=y^2/25=(5 x^2 + 3 y^2)/(45+75)=(10 x^2 -3 y^2)/(90-75) do đó (5 x^2 + 3y^2)/(10 x^2 - 3 y^2)=(45+75)/(90-75)=8

Ta có: \(\dfrac{x}{y}=\dfrac{3}{5}\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}\)

Đặt \(\dfrac{x}{3}=\dfrac{y}{5}=k\)

\(\Rightarrow x=3k\)

\(y=5k\)

Khi đó \(P=\dfrac{5x^2+3y^2}{10x^2-3y^2}=\dfrac{5.\left(3k\right)^2+3.\left(5k\right)^2}{10.\left(3k\right)^2-3.\left(5k\right)^2}\)

\(=\dfrac{5.9k^2+3.25k^2}{10.9k^2-3.25k^2}=\dfrac{45k^2+75k^2}{90k^2-75k^2}\)

\(=\dfrac{120k^2}{15k^2}=\dfrac{120}{15}=8.\)

\(\dfrac{x}{y}=\dfrac{3}{5}\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}\Rightarrow x=3k;y=5k\)

\(P=\dfrac{5x^2+3y^2}{10x^2-3y^2}\)

\(P=\dfrac{5.3k^2+3.5k^2}{10.3k^2-3.5k^2}\)

\(P=\dfrac{15k^2+15k^2}{30k^2-15k^2}\)

\(P=\dfrac{30k^2}{15k^2}=2\)

đặt \(\frac{x}{3}=\frac{y}{5}=k\)(k khac 0)

 Từ  \(\frac{x}{3}=k\)=>x=3k

        \(\frac{y}{5}=k\)=>y=5k

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