Solve. (-3)/(2 x+5)=(2)/(x-1)

Name: Problem 28, Chapter 11: Prealgebra and Introductory Algebra
Uploaded: 2020-06-24T21:01:44-08:00
Duration: 1 min 10 s
Channel: Cory Kuzinski
Description: Solve. (-3)/(2 x+5)=(2)/(x-1)

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Key Concepts

Rational Equations

Rational equations are equations containing one or more fractions whose numerators and denominators are polynomials. Solving them often involves finding a common denominator or using other strategies to eliminate the fractions, enabling you to work with a simpler equation, usually a polynomial equation. Understanding rational equations is important because they frequently appear in various branches of mathematics and applied problems.

Cross Multiplication

Cross multiplication is a technique used to solve equations that have two rational expressions set equal to each other. By multiplying each side of the equation by the product of the denominators, you can eliminate the fractions and convert the equation into a simpler form, often a linear or quadratic equation. This method is particularly effective when each side of the equation consists of a single fraction.

Domain Restrictions

Domain restrictions refer to the values that are not allowed in the solution of an equation because they would make any denominator equal to zero. When dealing with rational equations, it is essential to identify these restrictions before solving the equation to ensure that any proposed solutions are valid and do not result in division by zero. Checking for these restrictions helps prevent the inclusion of extraneous solutions.

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