Simplify each rational expression. (b^2+5 b-14)/(b^2+4 b-12)...

Name: Problem 32, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-06-18T07:42:19-08:00
Duration: 1 min 25 s
Channel: Ankit Gupta
Description: Simplify each rational expression. (b^2+5 b-14)/(b^2+4 b-12)

Key Concepts

Domain Restrictions

Domain restrictions are conditions that ensure the denominator of a rational expression is not equal to zero, as division by zero is undefined. When simplifying rational expressions, it is essential to identify and state values that must be excluded from the domain, even if those factors are canceled during the simplification process.

Cancellation of Common Factors

Once the polynomials in the numerator and denominator are factored, any common factors can be canceled out to simplify the rational expression. This process is analogous to reducing numerical fractions and simplifies the expression further, though it is important to note that factors canceled out correspond to values that are not allowed in the domain of the original expression.

Factoring Quadratic Expressions

Factoring quadratic expressions involves rewriting a quadratic polynomial as a product of two binomials. This is a fundamental algebraic technique that simplifies expressions and aids in solving equations or simplifying rational expressions. It requires identifying two numbers that multiply to the constant term while summing to the coefficient of the linear term.

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding how to work with rational expressions involves performing operations similar to those with numerical fractions, such as simplifying by factoring and canceling common factors, while considering any restrictions on the domain to avoid division by zero.

Transcript

Please give Ace some feedback