Multiply, and then simplify, if possible. See Example 3. (2 x^2-x-3)/(x^2-1) ·(x^2+x-2)/(2 x^2+x

step 1 For this exercise, we have 2x minus 3, x plus 1, x plus 2, and x minus 2. Then we divide this by

Multiply, and then simplify, if possible. See Example 3. (2...

Key Concepts

Rational Expressions

A rational expression is a fraction in which both the numerator and the denominator are polynomials. Understanding these expressions involves operations such as addition, subtraction, multiplication, and division, as well as simplification by factoring and canceling common factors.

Multiplication of Rational Expressions

When multiplying rational expressions, the operation involves multiplying the numerators together to form a new numerator and multiplying the denominators together to form a new denominator. This process requires factoring the resulting expressions to identify and cancel any common factors, often simplifying the expression considerably.

Polynomial Factorization

Polynomial factorization is the process of expressing a polynomial as a product of its factors. This is a fundamental skill when simplifying rational expressions because factoring allows one to break down both the numerator and denominator into simpler components that may share common factors.

Cancellation of Common Factors

Cancellation of common factors involves reducing a rational expression by eliminating factors that appear in both the numerator and the denominator. This is only valid when these factors are nonzero, ensuring that the simplified expression is equivalent to the original within its domain.

Domain Restrictions

Domain restrictions identify the values for which a rational expression is not defined, typically where the denominator is zero. Recognizing these restrictions is crucial because simplification does not change the domain of the original expression, even if common factors that cause zeros are canceled.

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