Answer:
2x + 1
Step-by-step explanation:

Factor out 2x² - 5x-3

divide x - 3 by x - 3
=> 2x + 1
<em><u>Or another step</u></em>
Step by Step Solution
STEP
1
:
Equation at the end of step 1
 
STEP
2
:
 2x² - 5x - 3/ x - 3 
Trying to factor by splitting the middle term
 2.1 Factoring 2x² - 5x - 3 
The first term is, 2x² its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -3 
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6 
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .
 -6 + 1 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1 
 2x² - 6x + 1x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
 2x • (x-3)
 Add up the last 2 terms, pulling out common factors :
 1 • (x-3)
Step-5 : Add up the four terms of step 4 :
 (2x+1) • (x-3)
 Which is the desired factorization
Canceling Out :
 2.2 Cancel out (x-3) which appears on both sides of the fraction line.
Final result :
 2x + 1