The expression $\frac{5x + 3}{6x (x + 1)}$ will be undefined when x equals

Analyze the question: A fraction is undefined when its denominator equals zero (division by zero is not allowed). So we find the values of x that make the denominator 0.

Concept: For a fraction a/b, b ≠ 0. Set the denominator equal to zero and solve.

Solution:

Denominator: 6x(x + 1) = 0

Using the zero product rule, either:

• 6x = 0, so x = 0
• x + 1 = 0, so x = -1

So the expression is undefined when x = {0, -1}.

Check:

• x = 0: denominator = 6(0)(1) = 0 ✔
• x = -1: denominator = 6(-1)(0) = 0 ✔

Note that the numerator 5x + 3 does not matter here. It would only matter if we were asked when the expression equals zero (x = -3/5).

Tip: "Undefined" means the denominator is zero, while "equals zero" means the numerator is zero. Don't mix them up in the exam. Also watch the signs: x + 1 = 0 gives x = -1, not 1.