Add or subtract as indicated. (5)/(9-x^2)-(4)/(x^2+4 x+3) |...

Name: Problem 56, Chapter 5: Intermediate Algebra
Uploaded: 2020-06-30T05:19:52-08:00
Duration: 2 min 33 s
Channel: Ankit Gupta
Description: Add or subtract as indicated. (5)/(9-x^2)-(4)/(x^2+4 x+3)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Rational Expressions

Rational expressions are fractions that consist of polynomials in the numerator and the denominator. The manipulation and simplification of these expressions require a careful treatment of the algebraic forms, particularly when performing operations such as addition or subtraction.

Polynomial Factorization

Polynomial factorization involves rewriting a polynomial as a product of simpler polynomials. This technique is essential when dealing with rational expressions because it allows one to break down complicated denominators into factors that can reveal common denominators or simplify the overall expression.

Finding a Common Denominator

When adding or subtracting rational expressions, it is necessary to find a common denominator. This requires determining the least common multiple of the individual denominators, often by factoring them, to combine the expressions into a single fraction.

Simplification of Algebraic Expressions

After establishing a common denominator and combining the expressions, the next crucial step is the simplification of the resulting algebraic expression. This involves combining like terms and canceling out common factors to reach the simplest form of the expression.

Transcript

Please give Ace some feedback