Question

Simplify each expression. $\frac{3 t^{2}}{t+2} \cdot \frac{t+2}{t^{2}}$

   Simplify each expression.
$\frac{3 t^{2}}{t+2} \cdot \frac{t+2}{t^{2}}$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 8, Problem 26

Instant Answer

Solved by Expert Elizabeth Xu

03/04/2020

Step 1

We can simplify this product by cancelling out the common factors in the numerator and the denominator. Show more…

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Simplify each expression. $\frac{3 t^{2}}{t+2} \cdot \frac{t+2}{t^{2}}$

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Key Concepts

Rational Expressions

Rational expressions are fractions in which the numerator and the denominator are polynomials. This concept is fundamental in algebra, where operations such as addition, subtraction, multiplication, and division are performed on these expressions. Understanding the structure of rational expressions helps in simplifying and solving algebraic equations effectively.

Multiplication of Fractions

Multiplication of fractions, including rational expressions, involves multiplying the numerators together and the denominators together. This process is guided by the same rules as multiplying numerical fractions and is a key technique employed in simplifying complex expressions by combining and reducing them.

Cancellation of Common Factors

Cancellation of common factors is a crucial technique used to simplify rational expressions. When a common factor appears in both the numerator and the denominator, it can be canceled out, provided it is not equal to zero. This step simplifies the expression and makes it easier to work with, particularly when solving equations.

Exponent Rules

Exponent rules govern how to handle expressions that involve powers of variables. These rules facilitate the simplification of expressions by allowing one to combine or reduce terms with the same base. Mastery of exponent laws, such as the quotient rule, is essential when simplifying rational expressions that include polynomial terms.

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