After some algebraic handling, the algebraic expression for x in terms of r is x = 1 / r + 1 .
How to clear a variable within an algebraic formula
In this question we must make use of algebra properties to clear a variable within a formula only formed by algebraic form, there are no trascendent functions herein. Clearing variables consists in leaving such variables alone in one side of the equivalence. Now we proceed to present the procedure in detail:
- r = 1 / (x - 1) Given
- r = (x - 1)⁻¹ Definition of division
- x - 1 = r⁻¹ Compatibility with multiplication / Existence of multiplicative inverse / Associative, commutative and modulative properties.
- x = 1 / r + 1 Definition of division / Compatibility with addition / Existence of additive inverse / Commutative and modulative properties / Result
Remark
The statement presents a typing omission, correct form is shown below:
Solve the equation r = 1 / (x - 1) for x in terms of r.
To learn more on rational functions: https://brainly.com/question/27914791
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