Find the Domain (3x(x-1))/(2x^2-5x-3)

Problem

Domain of (3*x*(x−1))/(2*x2−5*x−3)

Solution

1. Identify the condition for the domain of a rational function, which requires that the denominator cannot be equal to zero.

2*x2−5*x−3≠0

2. Factor the quadratic expression in the denominator by finding two numbers that multiply to −6 (the product of 2 and −3 and add to −5

2*x2−6*x+x−3≠0

2*x*(x−3)+1*(x−3)≠0

(2*x+1)*(x−3)≠0

3. Solve for the values of x that make the denominator zero by setting each factor to zero.

2*x+1=0⇒x=−1/2

x−3=0⇒x=3

4. Exclude these values from the set of all real numbers to define the domain.

x≠−1/2,x≠3

Final Answer

Domain: *{[x∈ℝ,x≠−1/2,x≠3]}

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