Answer:
[tex]\displaystyle \frac{45x+40}{2\sqrt{3x+4}}[/tex]
Step-by-step explanation:
Root Simplification
We are given the expression
[tex]\displaystyle 5\sqrt{3x+4}+\frac{15x}{2(3x+4)^{-1/2}}[/tex]
Converting the fractional power to square root
[tex]\displaystyle 5\sqrt{3x+4}+\frac{15x}{2\sqrt{3x+4}}[/tex]
Adding both terms as fractions
[tex]\displaystyle \frac{10\left (\sqrt{3x+4}\right )^2+15x}{2\sqrt{3x+4}}[/tex]
Simplifying the square root
[tex]\displaystyle \frac{10(3x+4)+15x}{2\sqrt{3x+4}}[/tex]
Operating and reducing
[tex]\displaystyle \frac{30x+40+15x}{2\sqrt{3x+4}}[/tex]
[tex]\displaystyle \boxed{\frac{45x+40}{2\sqrt{3x+4}}}[/tex]
