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HomeHomework HelpmathematicsRational Expression Simplification

Rational Expression Simplification

Rational expression simplification involves reducing complex fractions to their simplest form by eliminating common factors and canceling out denominators. This topic covers methods such as factoring, canceling, and multiplying by reciprocal fractions. Understanding rational expression simplification is crucial in Mathematics as it enables students to solve equations, manipulate expressions, and model real-world problems.

intermediate
2 hours
Mathematics
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Overview

Rational expression simplification is a vital skill in mathematics that involves reducing fractions with polynomial numerators and denominators to their simplest form. This process requires a solid understanding of factoring, identifying common factors, and canceling them appropriately. Mastering th...

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Key Terms

Rational Expression
A fraction where the numerator and denominator are polynomials.

Example: 1/(x^2 - 1)

Polynomial
An expression consisting of variables raised to whole number powers and coefficients.

Example: 3x^2 + 2x - 5

Factoring
The process of breaking down a polynomial into simpler components that multiply to give the original polynomial.

Example: x^2 - 9 = (x - 3)(x + 3)

Common Factor
A number or expression that divides two or more numbers or expressions without leaving a remainder.

Example: In 6x and 9x, the common factor is 3x.

Canceling
The process of removing common factors from the numerator and denominator of a fraction.

Example: In (2x)/(4x), canceling gives 1/2.

Greatest Common Factor (GCF)
The largest factor that two or more numbers or expressions share.

Example: The GCF of 8 and 12 is 4.

Related Topics

Algebraic Fractions
Study of fractions that contain algebraic expressions.
intermediate
Polynomial Functions
Exploration of functions defined by polynomials.
intermediate
Complex Fractions
Fractions that have fractions in the numerator, denominator, or both.
advanced
Rational Equations
Equations that involve rational expressions.
intermediate

Key Concepts

FactoringCommon FactorsCancelingPolynomial Division