Answer
$\dfrac{(2x+5)(4x^{2}+5x-8)}{(x^{2}-4)^{1/2}}$
Work Step by Step
$x(2x+5)^{2}(x^{2}-4)^{-1/2}+2(x^{2}-4)^{1/2}(2x+5)$
Take out common factor $(2x+5)(x^{2}-4)^{-1/2}$ from the expression:
$x(2x+5)^{2}(x^{2}-4)^{-1/2}+2(x^{2}-4)^{1/2}(2x+5)=...$
$...=(2x+5)(x^{2}-4)^{-1/2}[x(2x+5)+2(x^{2}-4)]=...$
Simplify the expression inside brackets:
$...=(2x+5)(x^{2}-4)^{-1/2}(2x^{2}+5x+2x^{2}-8)=...$
$...=(2x+5)(x^{2}-4)^{-1/2}(4x^{2}+5x-8)=...$
Change the sign of the exponent of $x^{2}-4$ by putting the factor as a denominator:
$...=\dfrac{(2x+5)(4x^{2}+5x-8)}{(x^{2}-4)^{1/2}}$
