Simplify each rational expression. (a^2+7 a+10)/(a^2-7 a-18)...

Name: Problem 23, Chapter 4: Intermediate Algebra
Uploaded: 2022-02-27T23:24:26-08:00
Duration: 18 s
Channel: Erika Bustos
Description: Simplify each rational expression. (a^2+7 a+10)/(a^2-7 a-18)

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Key Concepts

Domain Restrictions in Rational Expressions

When simplifying rational expressions, it is important to consider the values for which the expression is undefined. These typically occur where the denominator equals zero. Identifying and excluding these values ensures that any simplification or cancellation does not change the domain of the original expression.

Factoring Quadratic Expressions

This concept involves rewriting quadratic expressions as a product of two binomials. By finding two numbers that multiply to give the constant term and add to give the coefficient of the linear term, a quadratic can be decomposed into factors. This process is essential in simplifying expressions and solving quadratic equations.

Simplifying Rational Expressions

Simplifying rational expressions means reducing a fraction where both the numerator and the denominator are polynomials to its simplest form. This is achieved by factoring the polynomials and then canceling out any common factors, provided the factors being canceled are not zero, ensuring that the expression is equivalent to the original.

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