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.