Question

Find any values for which the rational expression 4x + 4/x^2 - 2x - 8 is undefined.

a) ( x = 2 )
b) ( x = -2 )
c) ( x = 4 )
d) ( x = -4 )

Answer 1

The expression 4x + 4/x^2 - 2x - 8 is undefined when x = 4 and x = -2.

Step-by-step explanation:

The expression 4x + 4/x^2 - 2x - 8 is undefined when the denominator is equal to zero because division by zero is undefined. Therefore, to find the values for which the expression is undefined, we need to solve the equation x^2 - 2x - 8 = 0.

To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring gives us (x - 4)(x + 2) = 0, so the values x = 4 and x = -2 make the expression undefined.

In conclusion, the values for which the expression 4x + 4/x^2 - 2x - 8 is undefined are x = 4 and x = -2.