Question 5355
Set this up like a long division problem

(I am going to use the square root sign on the computer)

{{{(x+3) sqrt(2x^2+x-13)}}}
The steps for long division are:
Step 1. divide the first term of the numerator by the first term of the denominator
Step 2. multiply both terms in the denominator by the result of step 1.
Step 3. subtract the result of step 2 from the original numerator
Step 4. Bring the next number from the numerator down and add to the result of step 3

repeat the process 

perform the division part of the long division on the FIRST term of the numerator (the {{{2x^2}}} in the {{{(2x^2+x-13)}}} and the first term of the denominator (the X in the (x+3)) , but perform the multiplication and subtraction on BOTH terms in the denominator (both the x and the 3 in the (x+3) term):

Step 1.  divide {{{2x^2}}} by x and get 2x
Step 2. multiply (x+3) by 2x to get {{{2x^2+6x}}}
Step 3. subtract {{{2x^2+6x}}} from {{{2x^2+x-13}}} and get {{{-5x}}}
Step 4. Bring down the next term {{{-13}}} and add it to {{{-5x}}} to get {{{-5x-13}}}

Repeat:

Step 1. divide {{{-5x}}} by {{{x}}} to get {{{-5}}}
Step 2. multiply {{{- 5}}} by {{{x+3}}} to get {{{-5x-15}}}
Step 3. subtract {{{-5x-15}}} from {{{-5x-13}}} and get 2 as a remainder

The answer will is {{{2x-5}}} with a remainder of {{{2/(x+3)}}}