Identify the least common denominator of each group of...

Identify the least common denominator of each group of rational expression, and rewrite each as an equivalent rational expression with the LCD as its denominator.

$\frac{a}{24 a+36}, \frac{1}{18 a+27}$

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Key Concepts

Factorization

Factorization involves breaking down an expression into a product of simpler expressions or factors. In the context of rational expressions, factorization is critical for identifying common factors in denominators and for simplifying expressions as well as finding the least common denominator.

Equivalent Expressions

Equivalent expressions are different representations of the same mathematical quantity. When rewriting rational expressions with a common denominator, it is crucial to multiply the numerator and the denominator by appropriate factors to maintain the equality, ensuring that the new expression is equivalent to the original one.

Least Common Denominator (LCD)

The least common denominator is the smallest expression that can serve as a common denominator for two or more rational expressions. It is essential for combining or comparing rational expressions because it helps ensure that each fraction is expressed with a common base, facilitating operations like addition or subtraction.

Rational Expressions

Rational expressions are fractions in which the numerator and/or the denominator are polynomials. They require special techniques for operations such as addition, subtraction, multiplication, and division, highlighting the importance of understanding how these polynomials interact within a fraction.

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