Solve each equation for the specified variable. (Assume all denominators are nonzero.) 1/R=1/r_1 + 1/r_2, for R

Key Concepts

Reciprocal Relationships

In algebra, a reciprocal relationship involves the concept of fractions where the reciprocal of a number 'x' is '1/x'. This is particularly important in equations involving rates or resistances, as seen in the equation 1/R = 1/r_1 + 1/r_2, where R represents the total resistance in a parallel circuit formed by resistances r_1 and r_2.

Solving for a Variable

Solving for a variable means isolating that variable on one side of the equation. In the context of the given equation, we need to manipulate the equation to express R in terms of r_1 and r_2. This often involves algebraic operations such as addition, subtraction, multiplication, and division to rearrange the equation appropriately.

Nonzero Denominators

The assumption that all denominators are nonzero is crucial in algebraic equations involving fractions. It ensures that the operations performed do not lead to undefined expressions. In the context of the equation provided, it guarantees that r_1 and r_2 cannot be zero, which would make the terms 1/r_1 and 1/r_2 undefined, thus affecting the validity of the solution.