Question
What\:are\:the\:restrictions\:on\:the\:variable\:\frac{z^2+10z+25}{z^2-4z-45}
Answers
GPT 3.5
The variable in the given expression is denoted by "z".
To find the restrictions on the variable "z", we must consider the denominator of the fraction, which is z^2 - 4z - 45.
For a fraction to be defined, the denominator cannot be equal to zero. Therefore, we need to find the values of "z" that make the denominator zero and exclude them from the domain.
To solve the equation z^2 - 4z - 45 = 0, we can factor it as (z - 9)(z + 5) = 0.
Setting each factor to zero, we have z - 9 = 0 and z + 5 = 0, which gives z = 9 and z = -5, respectively.
Therefore, the restrictions on the variable "z" are z ≠ 9 and z ≠ -5. These values must be excluded from the domain to avoid division by zero.
To find the restrictions on the variable "z", we must consider the denominator of the fraction, which is z^2 - 4z - 45.
For a fraction to be defined, the denominator cannot be equal to zero. Therefore, we need to find the values of "z" that make the denominator zero and exclude them from the domain.
To solve the equation z^2 - 4z - 45 = 0, we can factor it as (z - 9)(z + 5) = 0.
Setting each factor to zero, we have z - 9 = 0 and z + 5 = 0, which gives z = 9 and z = -5, respectively.
Therefore, the restrictions on the variable "z" are z ≠ 9 and z ≠ -5. These values must be excluded from the domain to avoid division by zero.