find domain
a^2-b^2/a^2-3a * 2a-b/(a+b)^2
The domain of the given expression can be determined by looking at any possible values that would make the expression undefined.
To determine the domain of the expression, let's examine each individual term:
Term 1: (a^2 - b^2)/(a^2 - 3a)
The expression becomes undefined when the denominator is equal to 0, which occurs when:
a^2 - 3a = 0
a(a - 3) = 0
So, either a = 0 or (a - 3) = 0
Therefore, the values a = 0 and a = 3 must be excluded from the domain of this term.
Term 2: (2a - b)/(a + b)^2
The expression becomes undefined when the denominator is equal to 0, which occurs when (a + b)^2 = 0. However, no value of a or b will satisfy this equation since squaring any real number will result in a positive value. Therefore, there are no exclusions from the domain of this term.
Taking both terms into account, the domain of the given expression is all real numbers except a = 0 and a = 3.
simplify
a^2-b^2/a^2-3a * 2a-b/(a+b)^2
To simplify the expression, let's simplify each term separately:
Term 1: (a^2 - b^2)/(a^2 - 3a)
This can be factored as a difference of squares:
(a + b)(a - b)/(a(a - 3))
This can be further simplified by canceling out common factors:
(a + b)/(a - 3)
Term 2: (2a - b)/(a + b)^2
Now that we have simplified both terms, we can multiply them together:
(a + b)/(a - 3) * (2a - b)/(a + b)^2
We can cancel out the common factor of (a + b) in the numerator and denominator:
1/(a - 3) * (2a - b)/(a + b)
This can be further simplified by multiplying the numerators and the denominators:
(2a - b)/(a - 3)(a + b)
Therefore, the simplified expression is: (2a - b)/(a - 3)(a + b)
find domain
a^2-b^2/a^2-3a * 2a-b/(a+b)^2
To find the domain of the given expression, we need to identify any values of a and b that would make the expression undefined.
Let's analyze each term separately:
Term 1: (a^2 - b^2)/(a^2 - 3a)
The expression becomes undefined when the denominator, a^2 - 3a, is equal to 0. To find the values of a that make the denominator 0, we can set a^2 - 3a = 0 and solve for a:
a(a - 3) = 0
a = 0 or a = 3
Term 2: (2a - b)/(a + b)^2
The expression becomes undefined when the denominator, (a + b)^2, is equal to 0. However, there are no values of a and b that will make this denominator equal to 0 since the square of any real number is always positive.
Therefore, the domain of the given expression is all real numbers except a = 0 and a = 3.
no
Apologies for the incorrect response. Let's reanalyze the expression.
To determine the domain of the given expression, we need to identify any values of a and b that would make the expression undefined.
Let's analyze each term separately:
Term 1: (a^2 - b^2)/(a^2 - 3a)
This expression becomes undefined when the denominator, a^2 - 3a, is equal to 0. Hence, we solve for a:
a^2 - 3a = 0
a(a - 3) = 0
This equation yields two potential values for a: a = 0 and a = 3.
Term 2: (2a - b)/(a + b)^2
This expression becomes undefined when the denominator, (a + b)^2, is equal to 0. To find values for a and b that satisfy this, we solve:
(a + b)^2 = 0
(a + b)(a + b) = 0
This equation is satisfied when a + b = 0. Therefore, this term is undefined when a = -b.
Combining both terms, we find that the expression is undefined when:
a = 0, a = 3, and a = -b.
Hence, the domain of the given expression is all real numbers except when a = 0, a = 3, and a = -b.