Question

algebra: concepts and connections - plc
adding and subtracting rational expressions (continued)
what is the least common denominator that can be used to add \\(\frac{x + 1}{8x^2}\\) and \\(\frac{2x - 3}{12x}\\)?
\\(96x^2\\)
\\(24x^3\\)
\\(96x^3\\)
\\(24x^2\\)

Explanation:

Step1: Factor denominators

Denominator 1: $8x^2 = 2^3 \cdot x^2$
Denominator 2: $12x = 2^2 \cdot 3 \cdot x$

Step2: Find LCM of constants

Take highest power of each prime: $2^3 \cdot 3 = 24$

Step3: Find LCM of variable terms

Take highest power of $x$: $x^2$

Step4: Multiply LCM components

$\text{LCM} = 24 \cdot x^2 = 24x^2$

Answer:

$24x^2$