Chapter 0: Chapter 0

Problem 1

As a single rational expression, simplified as much as possible. $$ \frac{x-4}{x+1} \cdot \frac{2 x+1}{x-1} $$

Short Answer

Expert verified

As a single rational expression, simplified as much as possible, we have: $\frac{x - 4}{x + 1} \cdot \frac{2x + 1}{x - 1} = \frac{2x^2 - 7x - 4}{x^2 - 1}$.

See the step by step solution

Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Multiplying the numerators

To multiply the rational functions, we need to multiply the numerators together and the denominators together. In this case, we have $(x - 4) \cdot (2x + 1)$ for the numerator of the result.

Step 2: Expanding the numerator

Now we will expand the multiplication in the numerator by applying the distributive property: \[ (x - 4)(2x + 1) = x(2x + 1) - 4(2x + 1) \]

Step 3: Applying distributive property on the numerator

Now we apply the distributive property again on each part of the multiplication: \[ x(2x + 1) - 4(2x + 1) = 2x^2 + x - 8x - 4 \]

Step 4: Simplifying the numerator

Combine the like terms in the numerator: \[ 2x^2 + x - 8x - 4 = 2x^2 - 7x - 4 \]

Step 5: Multiplying the denominators

Now for the denominator of the result, we simply multiply the two given denominators together: $(x + 1)(x - 1)$.

Step 6: Expanding the denominator

We can use the difference of squares formula to expand the denominator: \[ (x + 1)(x - 1) = x^2 - 1 \]

Step 7: Putting it all together

Combine the simplified numerator and denominator of the result to obtain the final expression: \[ \frac{2x^2 - 7x - 4}{x^2 - 1} \] So as a single rational expression, simplified as much as possible, we have: \[ \frac{x - 4}{x + 1} \cdot \frac{2x + 1}{x - 1} = \frac{2x^2 - 7x - 4}{x^2 - 1} \]

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Recommended explanations on Math Textbooks

Select your language

Chapter 0: Chapter 0

As a single rational expression, simplified as much as possible. $$ \frac{x-4}{x+1} \cdot \frac{2 x+1}{x-1} $$

Short Answer

Step by step solution

Unlock all solutions

Step 1: Multiplying the numerators

Step 2: Expanding the numerator

Step 3: Applying distributive property on the numerator

Step 4: Simplifying the numerator

Step 5: Multiplying the denominators

Step 6: Expanding the denominator

Step 7: Putting it all together

Access millions of textbook solutions in one place

Most popular questions from this chapter

More chapters from the book ‘Finite Mathematics and Applied Calculus’

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Statistics

Geometry

Pure Maths

Calculus