Solve: (x+1)/(x)-(x)/(x+1)=2

Name: Problem 37, Chapter 6: Algebra and Trigonometry
Uploaded: 2021-07-02T22:42:35-08:00
Duration: 1 min 31 s
Channel: Kimberly Waterbury
Description: Solve: (x+1)/(x)-(x)/(x+1)=2

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Key Concepts

Rational Equations

Rational equations are equations that involve fractions whose numerators and/or denominators are algebraic expressions. Solving these equations requires careful manipulation of the expressions to combine, compare, and simplify them, often after addressing any potential restrictions on the variable.

Domain Restrictions

When working with rational expressions, it is essential to identify values that are not allowed because they make any denominator zero. These restrictions define the domain of the equation and ensure that solutions are valid and do not result in undefined expressions.

Clearing Denominators

Clearing denominators is a technique used to eliminate fractions from an equation by multiplying every term by a common denominator. This process converts the rational equation into a polynomial equation, which is typically easier to solve.

Quadratic Equations

After clearing denominators and simplifying the equation, the resulting equation may be quadratic in nature. Solving quadratic equations involves techniques such as factoring, using the quadratic formula, or completing the square. Care must be taken to check for extraneous solutions that might have been introduced during earlier steps.

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