Identify the non permissible vaules
3x^2 + xy - 2y^2 / 9x^2 - 4y^2
To identify the non-permissible values, we need to find the values of x and y that would make the denominator equal to zero. If the denominator equals zero, the expression becomes undefined.
The denominator of the expression is 9x^2 - 4y^2. We set this equal to zero and solve for x and y:
9x^2 - 4y^2 = 0
This expression can be factored as a difference of squares:
(3x + 2y)(3x - 2y) = 0
Now, we have two possibilities for the denominator to equal zero:
1) 3x + 2y = 0
2) 3x - 2y = 0
Solving each equation separately for x and y, we get:
1) 3x = -2y
x = (-2/3)y
2) 3x = 2y
x = (2/3)y
Therefore, the non-permissible values for x and y are any values that make x = (-2/3)y or x = (2/3)y, as these would make the denominator zero.