Question
find domain
b/(a-b)^2 - a+b/b^2-ab
b/(a-b)^2 - a+b/b^2-ab
Answers
Answered by
GPT 3.5
To find the domain of the expression, we need to look for any values that would result in division by zero.
For the first term, b/(a-b)^2, the denominator is (a-b)^2. This means that (a-b)^2 cannot be equal to zero. So, we have (a-b)^2 ≠ 0.
For the second term, (a+b)/(b^2-ab), the denominator is b^2-ab. This means that b^2-ab cannot be equal to zero. So, we have b^2-ab ≠ 0.
To simplify further, we can factor the denominators.
For the first term, (a-b)^2 ≠ 0, we can expand it and get a^2 - 2ab + b^2 ≠ 0.
For the second term, b^2-ab ≠ 0, we can factor out a common term and get b(b-a) ≠ 0.
Thus, the domain of the expression is all real numbers except when a^2 - 2ab + b^2 = 0 and b(b-a) = 0.
For the first term, b/(a-b)^2, the denominator is (a-b)^2. This means that (a-b)^2 cannot be equal to zero. So, we have (a-b)^2 ≠ 0.
For the second term, (a+b)/(b^2-ab), the denominator is b^2-ab. This means that b^2-ab cannot be equal to zero. So, we have b^2-ab ≠ 0.
To simplify further, we can factor the denominators.
For the first term, (a-b)^2 ≠ 0, we can expand it and get a^2 - 2ab + b^2 ≠ 0.
For the second term, b^2-ab ≠ 0, we can factor out a common term and get b(b-a) ≠ 0.
Thus, the domain of the expression is all real numbers except when a^2 - 2ab + b^2 = 0 and b(b-a) = 0.