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
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>