\frac{x^2-1}{5xy}\cdot \frac{x^2y}{1+x}
find domain
To find the domain of the expression, we need to identify any values of x that would make parts of the expression undefined.
In the first fraction, the denominator is 5xy. This fraction would be undefined if the denominator is equal to zero. Therefore, we need to find the values of x and y that would make the denominator zero.
Setting 5xy equal to zero gives us two possibilities: x = 0 or y = 0.
In the second fraction, the denominator is 1 + x. This fraction would be undefined if the denominator is equal to zero. Therefore, we need to find the value of x that would make the denominator zero.
Setting 1 + x equal to zero gives us one possibility: x = -1.
Therefore, the values of x and y that would make parts of the expression undefined are x = 0, y = 0, and x = -1.
The domain of the expression is all real numbers except x = 0, x = -1.