Question

Simplify each expression. $$ \frac{9 x+99}{x^{2}+11 x} $$

   Simplify each expression.
$$
\frac{9 x+99}{x^{2}+11 x}
$$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 7, Problem 36

Instant Answer

Solved by Expert Victor Salazar

02/07/2022

Step 1

In the numerator, the common factor is 9 and in the denominator, the common factor is x. So, we get: $$ \frac{9(x+11)}{x(x+11)} $$ Show more…

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Simplify each expression. $$ \frac{9 x+99}{x^{2}+11 x} $$

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Key Concepts

Rational Expressions

A rational expression is a fraction in which both the numerator and the denominator are polynomials. Understanding rational expressions involves knowing how to manipulate and simplify these fractions, which is a foundational concept in algebra and precalculus.

Factoring

Factoring is the process of breaking down a polynomial into a product of its simpler factors. This technique is essential when simplifying rational expressions since it often reveals common factors in the numerator and denominator that can be canceled.

Cancellation of Common Factors

Once the numerator and denominator of a rational expression are factored, common factors may appear in both parts. Cancelling these common factors simplifies the expression, although one must be careful with the domain of the original expression.

Domain Considerations

When simplifying rational expressions, it is important to note the values that make the denominator zero, as these values are not included in the domain. This step ensures that the simplified expression is equivalent to the original, even though the cancellation of common factors might obscure these restrictions.

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