Q25. Simplify each expression.聽4y28y... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q25. (page 728)

Simplify each expression.
$\frac{4 y^{2}}{8 y^{4} + 16 y^{3}}$

Short Answer

Expert verified

The simplified expression is $\frac{1}{2 y^{2} + 4 y}$ .

Step by step solution

Step 1. Define rational expression.

A rational expression is an algebraic expression whose numerator and denominator are polynomials. Also, division by 0 is undefined, so therefore, the polynomials in the denominator cannot be zero and the values for which the denominator is zero is termed as excluded values for the respective rational expression.

Step 2. Factor the expression.

Factor the numerator and denominator, using their greatest common factor in the expression $\frac{4 y^{2}}{8 y^{4} + 16 y^{3}}$ .

role="math" localid="1648041783563" $\frac{4 y^{2}}{8 y^{4} + 16 y^{3}} = \frac{4 y^{2}}{8 y^{3} (y + 2)} = \frac{4 y^{2}}{4 y^{2} (2 y) (y + 2)}$

Step 3. Simplify the expression.

Further simplify the expression.

$\frac{4 y^{2}}{8 y^{4} + 16 y^{3}} = \frac{4 y^{2}}{4 y^{2} (2 y) (y + 2)} = \frac{1}{(2 y) (y + 2)} = \frac{1}{2 y^{2} + 4 y}$

Therefore, the simplified expression is $\frac{1}{2 y^{2} + 4 y}$ .

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91影视

Simplify each expression.
$\frac{4 y^{2}}{8 y^{4} + 16 y^{3}}$

Short Answer

Step by step solution

Step 1. Define rational expression.

Step 2. Factor the expression.

Step 3. Simplify the expression.

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91影视

Simplify each expression.4y28y4+16y3

Short Answer

Step by step solution

Step 1. Define rational expression.

Step 2. Factor the expression.

Step 3. Simplify the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Decision Maths

Probability and Statistics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Simplify each expression.
$\frac{4 y^{2}}{8 y^{4} + 16 y^{3}}$