Question

Identify the non permissible vaules

3x^2 + xy - 2y^2 / 9x^2 - 4y^2

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.