Question

Solve the equation. $$ \frac{x+1}{x}=2 $$

   Solve the equation.
$$
\frac{x+1}{x}=2
$$

College Algebra with Modeling and Visualization

College Algebra with Modeling and Visualization

Gary K. Rockswold 4th Edition

Chapter 4, Problem 83

Instant Answer

Solved by Expert Priyanka Sadarangani

05/24/2021

Step 1

This gives us: $$ x\left(\frac{x+1}{x}\right) = 2x $$ which simplifies to: $$ x+1 = 2x $$ Show more…

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Solve the equation. $$ \frac{x+1}{x}=2 $$

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Key Concepts

Rational Equations

Rational equations are equations that involve rational expressions, which are ratios of two polynomials. These equations require careful manipulation because the variable appears in the denominator, and solving them often involves strategies like finding a common denominator or cross multiplying to eliminate fractions.

Domain Restrictions

When working with rational expressions, it is important to consider the domain restrictions, meaning values for the variable that would make any denominator equal to zero must be excluded. This ensures that no invalid or extraneous solutions are accepted in the final answer.

Cross Multiplication

Cross multiplication is a method used to solve rational equations by eliminating the fractions. This involves multiplying both sides of the equation by the denominator to obtain a simpler equation, often a linear equation, which can then be solved using basic algebraic techniques.

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