Question
Simplify each expression. State all non-permissible values
3 / 2𝑥 + 5 / 6𝑥^2
3 / 2𝑥 + 5 / 6𝑥^2
Answers
GPT 3.5
To simplify the expression, we will find a common denominator and add the fractions.
The denominators are 2𝑥 and 6𝑥^2. The common denominator is 6𝑥^2.
To find the numerator for the first fraction, we multiply by 3 to both the numerator and denominator:
(3 / 2𝑥)(3/3) = 9 / 6𝑥
The expression now becomes:
9 / 6𝑥 + 5 / 6𝑥^2
Since the denominators are the same, we can combine the fractions:
(9 + 5) / 6𝑥^2 = 14 / 6𝑥^2
Now, we can simplify the expression further:
14 / 6𝑥^2 = 7 / 3𝑥^2
The non-permissible values for this expression would be any value of 𝑥 that makes the denominator equal to zero. In this case, the expression has a denominator of 3𝑥^2, so the non-permissible values are when 𝑥 equals zero or when 𝑥 equals any value that makes 𝑥^2 equal to zero. Thus, the non-permissible values are 𝑥 = 0.
The denominators are 2𝑥 and 6𝑥^2. The common denominator is 6𝑥^2.
To find the numerator for the first fraction, we multiply by 3 to both the numerator and denominator:
(3 / 2𝑥)(3/3) = 9 / 6𝑥
The expression now becomes:
9 / 6𝑥 + 5 / 6𝑥^2
Since the denominators are the same, we can combine the fractions:
(9 + 5) / 6𝑥^2 = 14 / 6𝑥^2
Now, we can simplify the expression further:
14 / 6𝑥^2 = 7 / 3𝑥^2
The non-permissible values for this expression would be any value of 𝑥 that makes the denominator equal to zero. In this case, the expression has a denominator of 3𝑥^2, so the non-permissible values are when 𝑥 equals zero or when 𝑥 equals any value that makes 𝑥^2 equal to zero. Thus, the non-permissible values are 𝑥 = 0.