Answer
$\frac{7x-2y}{2x+5y}$
Work Step by Step
$7x^{2}=5y^{2}+4xy + 1$
Find dy/dx by implicit differentiation
$\frac{dx}{dy}(7x^{2}-5y^{2}-4xy)=\frac{dx}{dy}(1)$
$14x -10y\frac{dy}{dx} - 4x\frac{dy}{dx}−4y=0$
$(4x+10y)\frac{dy}{dx}=14x-4y$
$\frac{dy}{dx}=\frac{14x-4y}{4x+10y}=\frac{7x-2y}{2x+5y}$