Perform the indicated operation. Simplify, if possible. (4-a^2)/(a^2-9)-(a-2)/(3-a)

Name: Problem 65, Chapter 7: Elementary and Intermediate Algebra
Uploaded: 2020-05-20T22:08:43-08:00
Duration: 1 min 50 s
Channel: Karly Williams
Description: Perform the indicated operation. Simplify, if possible. (4-a^2)/(a^2-9)-(a-2)/(3-a)

step 1 Okay, we need to find our least common denominator. So we're just going to multiply these by neg

Perform the indicated operation. Simplify, if possible....

Key Concepts

Handling Sign Changes

In rational expressions, recognizing and managing sign differences is vital, especially when similar expressions with reversed terms appear in the numerator and denominator. Converting expressions so that factors match in both form and sign allows proper cancellation and simplification.

Finding a Common Denominator

When subtracting or adding rational expressions, a common denominator is necessary to combine the terms into a single expression. This involves expressing each rational term with the same denominator and then combining like terms in the numerator, often aided by prior factoring steps.

Difference of Squares

The difference of squares is a specific pattern in algebra where an expression of the form M² - N² can be factored into (M - N)(M + N). Recognizing this pattern allows for the rewriting of quadratic expressions, which can simplify rational expressions when these factors appear in both the numerator and the denominator.

Factoring Polynomials

Factoring is the process of rewriting a polynomial as a product of simpler polynomials. In the context of rational expressions, factoring both the numerator and denominator can reveal common factors that may be canceled. This technique is essential for simplifying expressions and solving equations.

Simplifying Rational Expressions

Simplifying rational expressions involves factoring both the numerators and denominators and then canceling any common factors. This process requires ensuring that the cancellation is valid by considering any restrictions on the variable (values that would make any denominator zero).

Transcript

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