Question

Simplify the expression. $$ \frac{2 x}{x-1}-\frac{7 x}{x+4} $$

   Simplify the expression.
$$
\frac{2 x}{x-1}-\frac{7 x}{x+4}
$$

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 11, Problem 41

Instant Answer

Solved by Expert Amy Jiang

04/23/2020

Step 1

The common denominator is the product of $(x-1)$ and $(x+4)$, which are the denominators of the two fractions. Show more…

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Simplify the expression. $$ \frac{2 x}{x-1}-\frac{7 x}{x+4} $$

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Key Concepts

Rational Expressions

Rational expressions are fractions where both the numerator and the denominator are polynomials. Understanding how to manipulate these expressions is fundamental in algebra, particularly when combining, adding, or subtracting them.

Common Denominator

When dealing with operations on rational expressions, finding the common denominator is essential. This involves identifying the least common multiple of the denominators, which allows you to rewrite the expressions with a shared denominator so they can be combined effectively.

Algebraic Manipulation

Algebraic manipulation refers to the process of expanding, factoring, and simplifying expressions. In the context of subtracting rational expressions, it involves distributing and combining like terms in the numerator after rewriting the fractions with a common denominator.

Domain Restrictions

Domain restrictions are important in rational expressions to avoid division by zero. When simplifying such expressions, it is crucial to note the values of the variable that would make any denominator equal to zero, thus being excluded from the set of permissible values.

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