Question 836632
{{{25x^2(4+x^2)^(-3/2) + 6x(4+x^2)^(-1/2) }}}

since {{{1/(sqrt(4+x^2)^3)=1/((4+x^2)sqrt(4+x^2)) }}} and {{{(4+x^2)^(-1/2)=1/sqrt(4+x^2) }}}, we have


{{{25x^2/((4+x^2)sqrt(4+x^2)) + 6x/sqrt(4+x^2)}}}


{{{25x^2/( (4+x^2)sqrt(4+x^2)) + 6x(4+x^2)/((4+x^2)sqrt(4+x^2))}}}


{{{(25x^2 + 6x(4+x^2))/((4+x^2)sqrt(4+x^2))}}}


{{{(25x^2 + 24x+6x^3)/((4+x^2)sqrt(4+x^2))}}}


{{{x(25x + 24+6x^2) /((4+x^2)sqrt(4+x^2))}}}....replace {{{(25x + 24+6x^2)}}} with {{{(2x+3)(3x+8)}}}


{{{ (x(2x+3)(3x+8))/((4+x^2)sqrt(4+x^2)) }}}