Question

Simplify the expression. $$\frac{4}{x+4}-\frac{7}{x-2}$$

   Simplify the expression.
$$\frac{4}{x+4}-\frac{7}{x-2}$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 11, Problem 19

Instant Answer

Solved by Expert Raushan Kumar

09/22/2020

Step 1

Step 1: First, we find the common denominator of the two fractions, which is $(x+4)(x-2)$. Show more…

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Simplify the expression. $$\frac{4}{x+4}-\frac{7}{x-2}$$

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Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. Simplifying these expressions involves performing algebraic operations to write them in a simpler or more reduced form while maintaining their equivalence.

Common Denominator

Finding a common denominator is a crucial step when combining or subtracting rational expressions. This involves determining the least common multiple of the denominators so that the expressions can be rewritten with a shared denominator, thereby allowing direct subtraction of the numerators.

Combining Like Terms

After rewriting with a common denominator, algebraic manipulation, such as combining like terms in the numerators, is necessary. This step simplifies the expression by consolidating similar terms, which can lead to further reduction or factoring.

Distributive Property

The distributive property is used to expand or factor expressions during the simplification process. It ensures that each term in one polynomial is correctly multiplied by each term in another, which is essential when dealing with complex numerators or denominators.

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