Question

Find the domain of the given rational expression:

3x-2/x²+5x-6

a) (-[infinity],-6)∪(-6,1)∪(1,[infinity])
b) (-[infinity],-6)∪(-6,0)∪(0,[infinity])
c) (-[infinity],-3)∪(-3,2)∪(2,[infinity])
d) (-[infinity],-5)∪(-5,2)∪(2,[infinity])

Answer 1

The domain of the given rational expression is (-∞,-6)∪(-6,1)∪(1,∞).

Step-by-step explanation:

The domain of a rational expression is the set of all real numbers that make the expression defined.

In this case, the expression is 3x-2/x^2+5x-6.

To find the domain, we need to determine the values of x that make the denominator zero.

By factoring the denominator, we get (x+6)(x-1).

Setting each factor equal to zero gives x = -6 and x = 1.

Therefore, the domain of the rational expression is the set of all real numbers except x = -6 and x = 1.

The correct answer is option a) (-∞,-6)∪(-6,1)∪(1,∞).