find the domain of the original expression
3x^2+15xy/x+5y
The domain of the original expression is all real numbers except for the values of x and y that make the denominator equal to zero.
So, the domain of the original expression is x ≠ -5y.
find the domain of the original expression
a-3b/a^2-3ab
To find the domain of the original expression, we need to consider the values of a and b that make the denominator equal to zero.
The denominator of the expression is a^2 - 3ab. Setting it equal to zero gives us:
a^2 - 3ab = 0
Factoring out a common factor of a, we get:
a(a - 3b) = 0
This equation will be satisfied if either a = 0 or (a - 3b) = 0.
Therefore, the domain of the original expression is:
a ≠ 0 and a ≠ 3b.
To find the domain of the expression (3x^2 + 15xy) / (x + 5y), we need to identify any values of x and y that would make the denominator equal to zero.
The expression has a denominator of (x + 5y). Setting this equal to zero and solving for x gives:
x + 5y = 0
x = -5y
So, any values of x and y that satisfy the equation x = -5y will make the denominator equal to zero, resulting in an undefined expression.
Therefore, the domain of the original expression is all real numbers except for x = -5y.