Answer:
<h3>The given expression can be written in the form 

 as 

 where  q(x)=

 , r(x)=0 and b(x)=x-3</h3>
Step-by-step explanation:
Given rational expression is 
<h3>To rewrite the given rational expression in the given form  and match their correct expressions:</h3>
Rewrite the given rational expression  in the form of
 in the form of  where q(x) is the quotient, r(x) is the remainder and b(x) is the divisor.
 where q(x) is the quotient, r(x) is the remainder and b(x) is the divisor.
<h3>Now solve the given expression by using Synthetic division, we get</h3>
Since x-3 is a factor for 
<h3>Therefore b(x)=x-3</h3>
3_|   2     -7     6     -9
        0      6    -3      9
    ------------------------------------
       2      -1       3      0
   ------------------------------------
Therefore we have quadratic equation 
<h3>q(x)=

</h3><h3>Remainder is 0</h3><h3>Therefore r(x)=0</h3>
Therefore we can write in the form as  
 
It is in the form of 
<h3>Therefore the given expression can be written in the form 

 as 

 where  q(x)=

 , r(x)=0 and b(x)=x-3</h3>