Question 919326

{{{p/q=(1/3)(sqrt((h+2k)/(3h+k)))}}}

make {{{h}}} the subject 

{{{(p/q)/(1/3)=sqrt((h+2k)/(3h+k))}}}

{{{3p/q=sqrt((h+2k)/(3h+k))}}} ......raise both sides to the power of two


{{{(3p/q)^2=(sqrt((h+2k)/(3h+k)))^2}}}


{{{9p^2/q^2=(h+2k)/(3h+k)}}} ........cross multiply


{{{9p^2(3h+k)=(h+2k)q^2}}}


{{{27p^2*h+9p^2*k=h*q^2+2k*q^2}}}



{{{27p^2*h-h*q^2=2k*q^2-9p^2*k}}}


{{{(27p^2-q^2)h=2k*q^2-9p^2*k}}}


{{{h=(2k*q^2-9kp^2)/(27p^2-q^2)}}}