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

1 Answer

3 votes

Answer:


\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))}

User TondaCZE
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