Final answer:
To find the numbers that must be excluded from the expression (x-2)/(x^2+8x+7), we set the denominator equal to zero and solve for x: x^2+8x+7 = 0. By factoring the quadratic equation, we find that x=-1 and x=-7 must be excluded.
Step-by-step explanation:
To find the numbers that must be excluded from the expression (x-2)/(x^(2)+8x+7), we need to determine the values of x that would make the denominator equal to zero. This is because division by zero is undefined. To do this, we set the denominator equal to zero and solve for x:
x^(2)+8x+7 = 0
Now we can factor the quadratic equation:
(x+1)(x+7) = 0
Setting each factor equal to zero, we get:
x+1 = 0 ⇒ x = -1
x+7 = 0 ⇒ x = -7
Therefore, the numbers -1 and -7 must be excluded from the expression.