Determine whether each of the following is an equation or an...

Determine whether each of the following is an equation or an expression. If it is an equation, then solve it for its variable. If is an expression, perform the indicated operation.
$\frac{5}{x-1}-\frac{2}{x}$

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Key Concepts

Expression vs Equation

This concept distinguishes between an expression, which is a combination of variables and constants combined by operations without an equality sign, and an equation, which asserts that two expressions are equal by using an equals sign. Understanding this difference is fundamental in algebra because it determines whether one needs to solve for a variable or simply simplify the expression.

Rational Expressions

Rational expressions are fractions where the numerator and the denominator are polynomials. Mastery of rational expressions is crucial in algebra for operations like addition, subtraction, multiplication, and division, as well as for simplifying complex expressions by finding common denominators.

Common Denominator

When working with rational expressions, especially during addition or subtraction, the common denominator concept is applied to rewrite each fraction so that they have the same denominator. This step is essential for combining the fractions into a single simplified expression.

Simplification

Simplification is the process of rewriting an expression in a simpler or more concise form by combining like terms, canceling common factors, and performing arithmetic operations. Simplification is a key step in handling both numerical and algebraic expressions, including rational expressions.

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