Final answer:
The value of x which makes the expression undefined is when value of x is -3/4.. Option B is correct.
Step-by-step explanation:
To simplify the rational expression 9x^2/(36x^3 + 27x^2), we first factor out the greatest common factor from the denominator, which is 9x^2.
The expression then becomes (9x^2) / (9x^2(4x + 3)).
By cancelling out the 9x^2 terms, we get 1 / (4x + 3).
To find which values of x make the expression undefined, we look at the denominator of the simplified expression (4x + 3).
The expression is undefined when the denominator is zero.
Thus, we set (4x + 3) = 0 and solve for x, giving us x = -3/4.
Hence, option B is correct.
Complete question:
Simplify the following rational expression: 9x^2/(36x^3 + 27x^2) Which values of x make the expression undefined? A) x = 0 B) x = -3/4 C) x = 3 D) x = -6