help please

Part a)

For positive real numbers x, y, z and  what is the maximum possible value for

$\sqrt{\frac{3x+4y}{6x+5y+4z}} + \sqrt{\frac{y+2z}{6x+5y+4z}} + \sqrt{\frac{2z+3x}{6x+5y+4z}}?$
 

Part b)

Find $\frac {z} {x}$ if $(x, y, z)$ is a triple that gives the maximum value in Part a.