Solutions for the given system with fractions I have to solve in $\Bbb{R}$ the following system :
$$
\ \left\{
    \begin{array}{ll}
        \frac{y}{x}+\frac{x}{y}=\frac{17}{4}  \\
        x^2-y^2=25
    \end{array}
\right.$$
For this one I am stuck, I tried to use the fact that $x^2-y^2=(x-y)(x+y)$ and multiply by $x$ (or $y$) in line $1$ but fractions 'bother' me. Any hint are welcome.

Hint:
$$x/y=t\Rightarrow y/x=1/t$$
from first equation
$$t+1/t=17/4\iff 4t^2-17t+4=0$$
$$t_{1,2}=\frac{17\pm15}{8}=4,1/4$$
$x=4y$ or $y=4x$
from second equation
$$(4y)^2-y^2=25,y^2=5/3$$ 
