Hi, Modify your question as :

  _{[ ][ ]} [ 9 - f(x) ] / [ 3 - (x)^1/2 ] -  _{[ ][ ]}  6 / [ 3 - (x)^1/2 ]

Applying L'Hospital rule in first part, we get :

 _{[ ][ ]} [ - f '(x) ] / [ 1/2(x)^-1/2 ] -  _{[ ][ ]} 6 / [ 3 - (x)^1/2 ]

Now, put the limits in first part,

For, second part, rationalize the denominator with 3 + x^(1/2) and put the limits.

 

Hope you got it.