Question

real world connection
guided practice
an electrical circuit with three resistors
total resistance
\\(\frac{1}{r_t} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}\\)
combining rational expressions
at the beginning of this session, you learned that electricians use the resistance formula to find the total resistance of a parallel circuit.
suppose \\(r_1 = x\\) ohms, \\(r_2 = 2x\\) ohms, and \\(r_3 = 3x\\) ohms. solve for \\(r_t\\), the total
simplify to find \\(r_t\\).
\\(\frac{1}{r_t} = \frac{1}{x} + \frac{1}{2x} + \frac{1}{3x}\\)
find the lcm of the denominators.
type your answer and then click or tap done.
what is the lcm of \\(x\\), \\(2x\\), and \\(3x\\)?
lcm = \\(square\\)

Explanation:

Step1: Identify denominators

Denominators: x, 2x, 3x

Step2: Find LCM of coefficients and variables

Coefficients: 1,2,3 → LCM=6; Variables: x → LCM=x

Step3: Combine LCMs

LCM=6×x=6x

Answer:

6x