Question

Please help factor and simplify:
5\sqrt(3x+4)+(15x)/(2)(3x+4)^(-(1)/(2))

Answer 1

`\displaystyle (45x+40)/(2√(3x+4))`

Explanation:

Root Simplification

We are given the expression

`\displaystyle 5√(3x+4)+(15x)/(2(3x+4)^(-1/2))`

Converting the fractional power to square root

`\displaystyle 5√(3x+4)+(15x)/(2√(3x+4))`

Adding both terms as fractions

`\displaystyle (10\left (√(3x+4)\right )^2+15x)/(2√(3x+4))`

Simplifying the square root

`\displaystyle (10(3x+4)+15x)/(2√(3x+4))`

Operating and reducing

`\displaystyle (30x+40+15x)/(2√(3x+4))`

`\displaystyle \boxed{(45x+40)/(2√(3x+4))}`