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Question 252297: What is the domain of the variable x in the equation y = (3x + 5)/(2x^2 + 5x - 3)?
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! To find domain, all you need to do is ask two questions:
Question #1 "is the variable in a square root?" If no, move to question 2. If yes set the junk under the root >=0.
Question #2 "is the variable in the denominator?" If no, then you have answered no to both questions and you say "all reals". If yes, however, remember that the denominator can never = 0. So, we set denominator junk not = 0. This is what the question has.
step 1: factor -> 2X^2 + 5X - 3 not = 0. (2x-1)(x+3) not = 0.
step 2: solve each part for X.
2X-1 not = 0. X not equal 1/2.
X+3 not equal 0. X not equal -3.
we have our domains: all real except -2 and 1/2.
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