/*! 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 77 $$ \frac{3 c}{4 c-5}+\frac{5}{... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 77

$$ \frac{3 c}{4 c-5}+\frac{5}{4 c-5} $$

Short Answer

Expert verified
\(\frac{3c + 5}{4c - 5}\)

Step by step solution

01

- Identify Common Denominator

Notice that both fractions have the same denominator, which is \(4c-5\). The fractions are already written over a common denominator, so this can make the addition straightforward.
02

- Combine the Numerators

Since the denominators are the same, add the numerators directly: \(\frac{3c}{4c - 5} + \frac{5}{4c - 5} = \frac{3c + 5}{4c - 5}\).
03

- Simplify the Expression

The expression \(\frac{3c + 5}{4c - 5}\) cannot be simplified further because there are no common factors between the numerator and the denominator.

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.

Common Denominator
One of the fundamental steps in working with algebraic fractions is to find a common denominator. A common denominator is the shared multiple between the denominators of the fractions. It allows us to combine the fractions easily.

In this exercise, notice that both fractions already have a common denominator, which is \(4c-5\). This means we don鈥檛 need to do extra work to align the denominators.

When fractions share the same denominator, it simplifies the process of addition or subtraction. Always look out for this step before attempting to combine fractions.
Combining Fractions
Once you鈥檝e identified that the fractions have a common denominator, the next step is to combine them. To do this, simply add or subtract the numerators while keeping the denominator unchanged.

In our example, we add the numerators as follows: \( \frac{3c}{4c - 5} + \frac{5}{4c - 5} \) will combine to become \ \( \frac{3c+5}{4c-5} \.\).

Remember, combining fractions with the same denominator is straightforward:
  • Keep the common denominator
  • Add or subtract the numerators directly
Simplifying Algebraic Expressions
The final step in working with algebraic fractions is to simplify the resulting expression. Simplifying involves reducing the expression to its simplest form.

In our case, we started with \( \frac{3c+5}{4c-5} \), and saw that it cannot be simplified further because the numerator and the denominator do not share any common factors.

To ensure an expression is in its simplest form, check for:

  • Common factors in the numerator and the denominator
  • Opportunities to factorize and reduce the fraction

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

Solve the application problem provided. Mike, an experienced bricklayer, can build a wall in 3 hours, while his son, who is learning, can do the job in 6 hours. How long does it take for them to build a wall together?

Solve the application problem provided. Chester rode his bike uphil 24 miles and then back downhill at 2 mph faster than his uphill. If it took him 2 hours longer to ride uphill than downhill, what was his uphill rate?

Solve the application problem provided. Dana enjoys taking her dog for a walk, but sometimes her dog gets away, and she has to run after him. Dana walked her dog for 7 miles but then had to run for 1 mile, spending a total time of 2.5 hours with her dog. Her running speed was 3 mph faster than her walking speed. Find her walking speed.

Solve each proportion. $$\frac{2 p+4}{8}=\frac{p+18}{6}$$

Solve the application problem provided. Hudson travels 1080 miles in a jet and then 240 miles by car to get to a business meeting. The jet goes 300 mph faster than the rate of the car, and the car ride takes 1 hour longer than the jet. What is the speed of the car?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.