Question

Simplify. $$ \frac{2 x}{x-5}-\frac{x}{x+5} $$

   Simplify.
$$
\frac{2 x}{x-5}-\frac{x}{x+5}
$$

College Algebra with Modeling and Visualization

College Algebra with Modeling and Visualization

Gary K. Rockswold 4th Edition

Chapter 0, Problem 80

Instant Answer

Solved by Expert Erika Bustos

04/16/2021

Step 1

The common denominator is the product of the two denominators, which is $(x-5)(x+5)$. Show more…

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Simplify. $$ \frac{2 x}{x-5}-\frac{x}{x+5} $$

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Key Concepts

Domain Restrictions

Domain restrictions are the values of the variable that must be excluded to avoid division by zero in rational expressions. When working with such expressions, it is important to identify and exclude values that make any denominator zero to ensure the expression remains defined.

Common Denominator

Finding a common denominator is a key step in combining rational expressions. It involves determining an expression, often the least common multiple of the individual denominators, so that the numerators can be combined through addition or subtraction, facilitating further simplification of the expression.

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are both polynomials. They follow the rules of arithmetic for fractions, and simplifying them often involves factoring, reducing common factors, and managing domain restrictions to ensure the expression is valid.

Factoring Polynomials

Factoring is the process of breaking down a polynomial into a product of simpler polynomials that, when multiplied together, give back the original polynomial. This is a crucial technique in simplifying rational expressions because it can reveal common factors in the numerator and denominator that might be canceled out.

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