/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Multiply. Leave each answer in f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 12

Multiply. Leave each answer in factored form. $$\frac{x+2}{3 x-4} \cdot \frac{4}{5 x+6}$$

Short Answer

Expert verified
\(\frac{4(x + 2)}{(3x - 4)(5x + 6)}\)

Step by step solution

01

- Write the given expression

Start by writing down the given multiplication of fractions: divide the two fractions: the first fraction is \(\frac{x+2}{3x-4}\) and the second fraction is \(\frac{4}{5x+6}\) The expression, therefore, is \(\frac{x+2}{3x-4} \times \frac{4}{5x+6} = \)
02

- Multiply the numerators

To multiply two fractions, multiply the numerators together and the denominators together. For our numerators: \((x + 2) \times 4 \)The numerator of the product fraction is:\( (x + 2) \times 4 = 4(x + 2) \)
03

- Multiply the denominators

Next, multiply the denominators together: \((3x - 4) \times (5x + 6)\)so the denominator of the product fraction is: \((3x - 4) (5x + 6)\)
04

- Write the final factored product

Combine the results from steps 2 and 3 to write the final product as a single fraction in factored form: \(\frac{4(x + 2)}{(3x - 4)(5x + 6)}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

factored form
Factored form means expressing a mathematical expression as a product of its factors. This is useful because it simplifies the problem of multiplying fractions. Instead of expanding and simplifying the product, we keep each part of the expression in its simplest multiplicative form. In this exercise, we are asked to keep our final answer in factored form. This not only makes the multiplication process easier but also keeps our solutions tidy. For example, our final product is written as \( \frac{4(x + 2)}{(3x - 4)(5x + 6)} \).
numerators
The numerator is the top part of a fraction. When multiplying fractions, you first multiply the numerators together. In this exercise, we have two numerators: \( x+2 \) and \( 4 \). To multiply these numerators, we use the distributive property: \( (x + 2) \times 4 \). When finished, we get \( 4(x + 2) \). This product becomes the numerator of our final fraction.
denominators
The denominator is the bottom part of a fraction. Similar to the numerators, when multiplying fractions, you multiply the denominators together. In our exercise, we multiply \( 3x-4 \) and \( 5x+6 \). This multiplication is written as \( (3x - 4)(5x + 6) \). Notice that we keep the result in factored form without expanding it out. This helps keep our final answer neat and always follows the exercise instructions to leave answers in factored form.
multiplication
To multiply fractions, follow these steps:
  • Multiply the numerators together.
  • Multiply the denominators together.
  • Simplify if possible, but keep the result in factored form when required.
In this exercise, we first write down the initial multiplication: \( \frac{x+2}{3x-4} \times \frac{4}{5x+6} \). Then, we multiply the numerators and denominators separately: The numerator is \( 4(x + 2) \) and the denominator is \( (3x - 4)(5x + 6) \). Finally, we combine these into a single fraction, giving us our final answer: \( \frac{4(x + 2)}{(3x - 4)(5x + 6)} \).

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose that the number of customer complaints is inversely proportional to the number of employees hired. Will a firm reduce the number of complaints more by expanding from 5 to 10 employees, or from 20 to \(25 ?\) Explain. Consider using a graph to help justify your answer.

The drag force \(F\) on a boat varies jointly as the wetted surface area \(A\) and the square of the velocity of the boat. If a boat traveling \(6.5 \mathrm{mph}\) experiences a drag force of \(86 \mathrm{N}\) when the wetted surface area is \(41.2 \mathrm{ft}^{2}\), find the wetted surface area of a boat traveling 8.2 mph with a drag force of \(94 \mathrm{N}\)

For each pair of functions \(f\) and \(g,\) find all values of a for which \(f(a)=g(a)\). $$f(x)=\frac{12}{x^{2}-6 x+9}$$, $$g(x)=\frac{4}{x-3}+\frac{2 x}{x-3}$$

To prepare for Chapter \(8,\) review solving inequalities \((\text {Section } 2.6)\) Solve. $$ \frac{5-x}{2} \geq 1 $$

Find an equation of variation in which: \(y\) varies jointly as \(w\) and the square of \(x\) and inversely as \(z,\) and \(y=49\) when \(w=3, x=7\) and \(z=12\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.