Factor and simplify: 5\sqrt(3x+4)+(15x)/(2)(3x+4))/(2)) - id534152344591385, haleyehewitt2001

Ответ:

kamiyaharris1

15.01.2022

$\displaystyle \frac{45x+40}{2\sqrt{3x+4}}$

Step-by-step explanation:

Root Simplification

We are given the expression

$\displaystyle 5\sqrt{3x+4}+\frac{15x}{2(3x+4)^{-1/2}}$

Converting the fractional power to square root

$\displaystyle 5\sqrt{3x+4}+\frac{15x}{2\sqrt{3x+4}}$

Adding both terms as fractions

$\displaystyle \frac{10\left (\sqrt{3x+4}\right )^2+15x}{2\sqrt{3x+4}}$

Simplifying the square root

$\displaystyle \frac{10(3x+4)+15x}{2\sqrt{3x+4}}$

Operating and reducing

$\displaystyle \frac{30x+40+15x}{2\sqrt{3x+4}}$

$\displaystyle \boxed{\frac{45x+40}{2\sqrt{3x+4}}}$

0,0(0 оценок)