Question 386826
{{{6/p = 2 + p/(p+1)}}}
Use the common denominator, {{{p(p+1)}}}
{{{(6(p+1))/(p(p+1))=2*(p(p+1))/(p(p+1))+p^2/(p(p+1))}}}
{{{(6(p+1))/(p(p+1))-2*(p(p+1))/(p(p+1))-p^2/(p(p+1))=0}}}
{{{(6(p+1)-2*(p(p+1))-p^2)/(p(p+1))=0}}}
{{{(6p+6-2*(p^2+p)+p^2)/(p(p+1))=0}}}
{{{(6p+6-2p^2-2p-p^2)/(p(p+1))=0}}}
{{{(-3p^2+4p+6)/(p(p+1))=0}}}
{{{(3p^2-4p-6)/(p(p+1))=0}}}
The equation equals zero when the numerator equals zero.
{{{3p^2-4p-6=0}}}
{{{3p^2-4p+4-6=4}}}
Using the quadratic formula,
{{{p = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{p = (4 +- sqrt( (-4)^2-4*3*(-6) ))/(2*3) }}}
{{{p = (4 +- sqrt( 16+72 ))/(6) }}}
{{{p = (4 +- sqrt( 88 ))/(6) }}}
{{{p = (4 +- 2*sqrt( 22 ))/(6) }}}
{{{highlight(p = (2 +- sqrt( 22 ))/(3) )}}}