Question

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

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

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 95

Instant Answer

Solved by Expert Julie Silva

07/03/2021

Step 1

This gives us: \[1 \times (1 - \frac{1}{x}) = 1 \times (1 + \frac{1}{x})\] which simplifies to: \[1 - \frac{1}{x} = 1 + \frac{1}{x}\] Show more…

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

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Key Concepts

Solving Linear Equations

After simplifying a rational equation, it often reduces to a linear equation. Solving linear equations involves isolating the variable through systematic operations such as addition, subtraction, multiplication, or division to find the variable's value.

Cross Multiplication

Cross multiplication is a technique used to eliminate the fractions in an equation by multiplying both sides by the denominators. This method simplifies the equation into a form more manageable for standard algebraic techniques, provided that the denominators are not zero.

Rational Expressions

Rational expressions involve fractions where the numerator and denominator are polynomials. Understanding them is crucial because they often come with restrictions on the variable, particularly values that make the denominator equal to zero, leading to undefined expressions.

Domain Restrictions

When solving equations that include rational expressions, it is essential to identify values that would make any denominator zero. These restrictions ensure that any solutions obtained are valid within the context of the original equation.

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