Question

determine the lcd of each rational expression $\frac{2x - 1}{8x}$ $\frac{3x + 1}{2x^{2}}$ 8x 2x 8x² 2x²

Explanation:

Step1: Prime - factor denominators

$8x = 2\times2\times2\times x$ and $2x^{2}=2\times x\times x$.

Step2: Determine LCD

Take the highest - power of each factor. For the factor 2, the highest power is $2^{3}$ (from 8x), and for the factor x, the highest power is $x^{2}$ (from $2x^{2}$). So, $LCD = 2^{3}\times x^{2}=8x^{2}$.

Answer:

$8x^{2}$