Question

Solve each equation. $$ \frac{t}{t-1}=\frac{2}{t-1}+2 $$

   Solve each equation.
$$
\frac{t}{t-1}=\frac{2}{t-1}+2
$$

Precalculus

Raymond A. Barnett,… 7th Edition

Chapter 1, Problem 26

Instant Answer

Solved by Expert Nick Johnson

07/17/2021

Step 1

This gives us: $$ t = 2 + 2(t-1) $$ Show more…

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Solve each equation. $$ \frac{t}{t-1}=\frac{2}{t-1}+2 $$

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Key Concepts

Solving Linear Equations

After clearing the denominators, the resulting equation is typically a linear equation. The process then involves combining like terms and isolating the variable to find the solution to the equation.

Clearing Denominators

Clearing denominators is a technique used to eliminate fractions from an equation by multiplying both sides by the common denominator. This simplifies the equation into a form that is easier to solve, but care must be taken to ensure that the multiplication is valid within the domain.

Domain Restrictions

When working with equations involving rational expressions, it is crucial to identify the values that make any denominator zero and exclude those from the possible solutions. This step is essential to avoid undefined expressions.

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. In equations, these expressions need careful handling because their denominators must not be zero, which influences the domain of the solution.

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