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Understand when a fraction is undefined.

May 22, 2026Mathematics

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Understand when a fraction is undefined.
A fraction is undefined when its denominator is equal to zero. For the given expression $\frac{3x+2}{2x+1}$ , the denominator is $2x+1$ .
Set the denominator equal to zero.
To find the value of $x$ for which the expression is undefined, we set the denominator to zero:
$2x+1 = 0$
Solve for $x$ .
Subtract 1 from both sides of the equation:
$2x = -1$
Divide by 2:
$x = -\frac{1}{2}$
Compare with the given options.
The calculated value $x = -\frac{1}{2}$ matches option (b).

The final answer is \boxed{\text{(b) -\frac{1}{2}}}.

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