Add or subtract as indicated. Simplify the result, if possible. (x^2+9 x)/(x^2-2 x-3)+(5)/(3-x)

Name: Problem 70, Chapter 7: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-08T14:30:06-08:00
Duration: 1 min 48 s
Channel: Brandon Fox
Description: Add or subtract as indicated. Simplify the result, if possible. (x^2+9 x)/(x^2-2 x-3)+(5)/(3-x)

step 1 To add these together, let's first factor some of the parts here, the denominator especially. Le

Add or subtract as indicated. Simplify the result, if...

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Key Concepts

Simplification of Rational Expressions

After combining rational expressions, the resulting expression often contains common factors in the numerator and denominator that can be cancelled, provided that these factors are not zero. Simplification reduces the expression to its simplest form, making it easier to work with or interpret.

Factoring Polynomials

This concept involves rewriting a polynomial as a product of its factors. In rational expressions, particularly when dealing with quadratics, factoring is used to simplify the expressions by breaking them into simpler, multiplicative components, which can then reveal common factors between numerators and denominators.

Finding a Common Denominator

When adding or subtracting rational expressions, it is essential to rewrite each expression with a common denominator. This process often involves factoring the denominators to determine the least common multiple, which allows the expressions to be combined into a single rational expression.

Domain Restrictions

When working with rational expressions, it is important to determine the values for which the expression is defined. These restrictions come from setting the denominators not equal to zero, ensuring that any cancellation or manipulation does not obscure values that would make the original expression undefined.

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