Which of the following is a rational expression whose domain has a restriction of x≠−1?
Responses
x^2+6x+5/6x+6
the fraction with numerator x squared plus 6 x plus 5 and denominator 6 x plus 6 - this is the correct answer
√x/2x+2
the fraction with numerator square root of x and denominator 2 x plus 2 - this is the incorrect answer
6x^3+60/x
the fraction with numerator 6 x cubed plus 60 and denominator x - this is the incorrect answer
x+1/x^3 -this is the incorrect answer
explain how you would get x^2+6x+5/6x+6 as your correct answer
To determine the rational expression with a domain restriction of x ≠ -1, we need to find an expression where the denominator does not equal zero when x = -1.
In the expression x^2 + 6x + 5 / 6x + 6, if we plug in x = -1 into the denominator, we get:
6(-1) + 6 = -6 + 6 = 0.
Since the denominator becomes zero when x = -1, this expression does not satisfy the domain restriction of x ≠ -1. Therefore, the correct answer is none of the given options.