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

Thay vào biểu thức A ta được:

\(A=\frac{5.\left(\frac{3y}{5}\right)^2+3y^2}{10.\left(\frac{3y}{5}\right)^2-3y^2}=\frac{\frac{9y^2+15y^2}{5}}{\frac{18y^2-15y^2}{5}}=\frac{24y^2}{3y^2}=8\)

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

Ta có: \(A=\frac{5x^2+3y^2}{10x^2-3y^2}=\frac{5.\left(3k\right)^2+3.\left(5k\right)^2}{10.\left(3k\right)^2-3.\left(5k\right)^2}=\frac{45k^2+75k^2}{90k^2-75k^2}=\frac{k^2\left(45+75\right)}{k^2\left(90-75\right)}=\frac{120k^2}{15k^2}=8\)

x/3 = y/5 => y = 5/3.x => y^2 = 25/9.x^2 => 3y^2 = 25/3.y^2

=> A =(5x^2+25/3.x^2)/(10x^2-25/3.x^2) = 40/3.x^2 / 5/3.x^2 = 8

Vậy A = 8

Tk mk nha

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

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

qqqqqqqwertyu

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: 

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

24/5 nha kn với mk nhé mk ko có bạn.

Đề là rút gọn hay tìm x,y ?

tính giá trị biểu thức

\(=\frac{x+y}{2x-y}\)

Đặt x/3=y/5=k

=>x=3k; y=5k

\(A=\dfrac{5\cdot9k^2+3\cdot25k^2}{10\cdot9k^2-3\cdot25k^2}=\dfrac{5\cdot9+3\cdot25}{10\cdot9-3\cdot25}=8\)

Ta gọi: \(\frac{x}{3}=\frac{y}{5}=k\Rightarrow x=3k;y=5k\)

Thay x = 3k và y = 5k vào A ta có: \(A=\frac{5^2.\left(3k\right)^2+3^2.\left(5k\right)^2}{10^2.\left(3k\right)^2-3^2.\left(5k\right)^2}=\frac{25.9k^2+9.25k^2}{100.9k^2-9.25k^2}=\frac{9.25k^2\left(1+1\right)}{9.25k^2\left(4-1\right)}=\frac{2}{3}\)

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

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

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

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

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

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

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

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