Question

What are the excluded values for the expression (4x^3 - 6x^2) / (3x^2 - 7x)?

A) x = 0
B) x = 3
C) x = 7/3
D) x = 0 and x = 7/3

Answer 1

The excluded values for the expression (4x^3 - 6x^2) / (3x^2 - 7x) are x = 0 and x = 7/3, since these make the denominator equal to zero and the expression undefined.

Step-by-step explanation:

To find the excluded values of the expression (4x^3 - 6x^2) / (3x^2 - 7x), we must identify the values of x that make the denominator equal to zero, since division by zero is undefined in mathematics. We set the denominator 3x^2 - 7x equal to zero and solve for x:

3x^2 - 7x = 0

x(3x - 7) = 0

This equation is factored into two parts: x = 0 and 3x - 7 = 0. By solving these two equations, we find that x can be either 0 or 7/3 for the denominator to be zero. Therefore, the excluded values are x = 0 and x = 7/3.

Thus, the correct answer is D) x = 0 and x = 7/3.