find domain
(ab-b)/a - (ab-a)/b - (a^2-b^2)/ab
The given expression is:
(ab-b)/a - (ab-a)/b - (a^2-b^2)/ab
To find the domain, we need to identify any values of variables that would result in division by zero, which is undefined.
For the expression (ab-b)/a to be defined, a cannot be equal to zero.
Similarly, for the expression (ab-a)/b to be defined, b cannot be equal to zero.
Lastly, for the expression (a^2-b^2)/ab to be defined, neither a nor b can be equal to zero, as the numerator will then be zero as well.
Therefore, the domain of the given expression is all real numbers except zero for a and b:
a ≠ 0 and b ≠ 0.
To find the domain of the expression (ab-b)/a - (ab-a)/b - (a^2-b^2)/ab, follow these steps:
Step 1: Identify any restrictions on the variables.
In this expression, we have the variables "a" and "b". To determine the restrictions on these variables, we need to consider any denominators present in the expression.
In the given expression, we have the denominators "a" and "b" in the first two terms, and the denominator "ab" in the third term.
Step 2: Set the denominators equal to zero and solve for the variables.
For the first two terms, we set the denominators "a" and "b" equal to zero and solve for "a" and "b", respectively.
For a = 0, there is a restriction because division by zero is undefined.
For b = 0, there is also a restriction because division by zero is undefined.
Now, for the third term, the denominator is "ab". To find the restrictions on "a" and "b", we set "ab" equal to zero and solve:
ab = 0
Since the product of two numbers equals zero if and only if at least one of the numbers is zero, we have two cases:
Case 1: a = 0
In this case, there is a restriction because division by zero is undefined.
Case 2: b = 0
In this case, there is a restriction because division by zero is undefined.
Step 3: Combine the restrictions.
Combining the restrictions from Step 2, we find that both "a" and "b" cannot be equal to zero simultaneously.
Therefore, the domain of the given expression is all real numbers except when a = 0 and b = 0.