Core stretch Positive quantities satisfy $\dfrac{p-x}{q}=\dfrac{p}{p+x}$. Express $x$ in terms o

Question

Core stretch Positive quantities satisfy $\dfrac{p-x}{q}=\dfrac{p}{p+x}$. Express $x$ in terms of $p,q$. Given further that $p=5q$, find $x:q$.

Accepted Answer

$x=\sqrt{p(p-q)}$; $x:q=2\sqrt5:1$.

Rational rearrangement and a ratio