For the following equation, a. Write the value or values of the variable that make a denominator zero. TI in mind, solve the equation. \[ \frac{2}{5 x}+\frac{1}{4}=\frac{74}{10 x}-\frac{1}{3} \] a. Write the value or values of the variable that make a denominator zero. (Use a comma to separate answers as needed.)

To find the values of the variable \( x \) that make the denominators zero in the equation \[ \frac{2}{5x} + \frac{1}{4} = \frac{74}{10x} - \frac{1}{3}, \] we need to identify the denominators in the equation: 1. The first term has a denominator of \( 5x \). 2. The second term has a denominator of \( 4 \) (which does not affect \( x \)). 3. The third term has a denominator of \( 10x \). 4. The fourth term has a denominator of \( 3 \) (which does not affect \( x \)). The denominators that involve \( x \) are \( 5x \) and \( 10x \). To find the values that make these denominators zero, we set them equal to zero: 1. For \( 5x = 0 \): \[ x = 0 \] 2. For \( 10x = 0 \): \[ x = 0 \] Thus, the only value of \( x \) that makes a denominator zero is \( 0 \). **Answer:** 0