Question

Solve for $t: \frac{t+1 / t}{1 / t-1}=1$.

   Solve for $t: \frac{t+1 / t}{1 / t-1}=1$.

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 96

Instant Answer

Solved by Expert James Kiss

07/01/2020

Step 1

$t(t-1)\left(\frac{t+1 / t}{1 / t-1}\right) = t(t-1)(1)$ Show more…

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Solve for $t: \frac{t+1 / t}{1 / t-1}=1$.

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Key Concepts

Rational Equations

A rational equation involves fractions whose numerators and denominators are algebraic expressions. Solving these equations typically requires eliminating the fractions—often by multiplying through by a common denominator—to obtain a simpler equation without rational expressions.

Domain Restrictions

When dealing with rational expressions, it is essential to identify values of the variable that make any denominator equal to zero since these values are not allowed in the domain. Recognizing these restrictions prevents including extraneous solutions in the final answer.

Clearing Denominators

Clearing denominators is a technique used to simplify equations that contain fractions by multiplying every term by the least common denominator. This step is crucial in transforming the equation into a simpler form where standard algebraic methods can be applied to find the solution.

Simplification of Algebraic Expressions

Simplification involves combining like terms, reducing fractions, and performing necessary arithmetic operations to express an equation in its simplest form. This process is foundational in algebra as it facilitates the subsequent steps of solving the equation.

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