\text{If }\frac{x}{y}=\frac{11}{5}\text{, then find }\frac{x^2+y^2}{x^2-y^2}

The correct answer is 73/48.

We are given the ratio:
$\frac{x}{y}=\frac{11}{5}$

From this ratio, we can express $x$ in terms of $y$ by letting $x=11k$ and $y=5k$ for some non-zero constant $k$.

We need to find the value of the expression:
$\frac{x^2+y^2}{x^2-y^2}$

Substituting $x=11k$ and $y=5k$ into the expression, we get:
$\frac{{\left(11k\right)}^2+{\left(5k\right)}^2}{{\left(11k\right)}^2-{\left(5k\right)}^2}$

Simplify the squared terms:
$\frac{121k^2+25k^2}{121k^2-25k^2}$

Factor out and cancel $k^2$ from both the numerator and the denominator:
$\frac{k^2(121+25)}{k^2(121-25)}=\frac{121+25}{121-25}$

Calculate the final numbers:
$\frac{146}{96}$

Reduce the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
$\frac{146/2}{96/2}=\frac{73}{48}$