Question

(3x+1)/(x^2-6x-8) область определения

Answer 1

X^2-6x-8=0
d=6^2+4×8=36+32=68
x1=(6+2pod kornem17)/2=3+(2podkornem17)/3
x2=3-(2podkornem17)/3
otvet:(-besk;x2) u (x1;+besk)

Answer 2

To find the domain of the given expression, we need to identify any values of "x" that would make the denominator equal to zero. Division by zero is undefined, so we must exclude such values from the domain.

The expression is: (3x + 1) / (x^2 - 6x - 8)

The denominator is x^2 - 6x - 8. To find the values of "x" that would make the denominator zero, we need to solve the equation:

x^2 - 6x - 8 = 0

To factor this quadratic equation, we look for two numbers whose product is -8 and whose sum is -6. The numbers are -8 and +1.

(x - 8)(x + 1) = 0

Now, set each factor to zero and solve for "x":

x - 8 = 0 --> x = 8 x + 1 = 0 --> x = -1

So, the values x = 8 and x = -1 would make the denominator zero, which means they are not allowed in the domain of the expression.

Therefore, the domain of the given expression is all real numbers except x = 8 and x = -1. In interval notation, the domain can be written as:

Domain: (-∞, -1) ∪ (-1, 8) ∪ (8, ∞)