Question

Simplify. $$ \frac{x^{5 y}+3 x^{4 y}}{3 x^{3 y}+x^{4 y}} $$

Name: Problem 97, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-10-19T03:35:01-08:00
Duration: 1 min 20 s
Channel: Sneha Ravi
Description: Simplify. (x^5 y+3 x^4 y)/(3 x^3 y+x^4 y)

   Simplify.
$$
\frac{x^{5 y}+3 x^{4 y}}{3 x^{3 y}+x^{4 y}}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 97

Instant Answer

Solved by Expert Sneha Ravi

10/19/2020

Step 1

In this case, the common term is $x^{4y}$. $$ \frac{x^{5 y}+3 x^{4 y}}{3 x^{3 y}+x^{4 y}} = \frac{x^{4y}(x + 3)}{x^{3y}(3 + x)} $$ Show more…

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Simplify. $$ \frac{x^{5 y}+3 x^{4 y}}{3 x^{3 y}+x^{4 y}} $$

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Key Concepts

Simplification of Rational Expressions

This key concept involves reducing a fraction whose numerator and denominator are algebraic expressions. Through techniques like factoring common terms and applying laws of exponents, the rational expression is simplified by canceling out the common factors, provided the variables involved do not lead to division by zero.

Laws of Exponents

This concept involves using the rules for manipulating expressions with exponents, such as multiplying or dividing terms with the same base by adding or subtracting their exponents. It provides the algebraic foundation for reducing terms with exponential expressions in the numerator and denominator.

Factoring

Factoring is the process of identifying and extracting common factors from different terms within an algebraic expression. By pulling out common factors, the expression can often be rewritten in a simpler form, which is a crucial step in simplifying more complex algebraic fractions.

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