multiply or divide as indicated. (x^2-9)/(x^2) ·(x^2-3 x)/(x^2+x-12)

Name: Problem 17, Chapter 0: Algebra and Trigonometry
Uploaded: 2020-06-05T15:22:39-08:00
Duration: 4 min 34 s
Channel: Gladys Fowler
Description: multiply or divide as indicated. (x^2-9)/(x^2) ·(x^2-3 x)/(x^2+x-12)

step 1 For problem 17, we're given an expression, just like 15 and 16, where we have to determine the e

Multiply or divide as indicated. (x^2-9)/(x^2) ·(x^2-3...

Key Concepts

Difference of Squares

The difference of squares is a specific factoring technique used when a polynomial is expressed in the form a^2 - b^2. It factors into (a - b)(a + b) and is a valuable tool for simplifying expressions that include this pattern.

Factoring Polynomials

Factoring involves rewriting a polynomial as a product of simpler polynomials or expressions. This is a key step in simplifying rational expressions, as it allows the identification and cancellation of terms that appear in both the numerator and denominator.

Cancellation of Common Factors

After factoring both the numerator and denominator of rational expressions, common factors can be cancelled, provided they are not equal to zero. This cancellation simplifies the expression and is fundamental in the process of reducing rational expressions to their simplest form.

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. They are manipulated by performing operations such as addition, subtraction, multiplication, and division, with careful attention to the domain of the expression, especially avoiding division by zero.

Multiplication of Rational Expressions

Multiplication of rational expressions involves multiplying the numerators together to form a new numerator and the denominators together to form a new denominator. This process often creates opportunities for simplification through factoring and cancellation of common factors.

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