/*! 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 66 Simplify each rational expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 66

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{9 x-15}{5-3 x}$$

Short Answer

Expert verified
The simplified form of the rational expression \(\frac{9x - 15}{5 - 3x}\) is \(-3\).

Step by step solution

01

Factorizing Numerator and Denominator

The first step is to factorise the numerator and denominator separately. From the numerator \(9x - 15\), taking 3 as common yields \(3(3x - 5)\). In the denominator, \(5 - 3x\) can be rewritten as \(-1*(3x - 5)\) by taking -1 common.
02

Canceling Common Factors

The rational expression after factorization becomes \(\frac{3(3x - 5)}{-1*(3x - 5)}\). Now both the numerator and the denominator have a common term \((3x - 5)\), which can be cancelled from the top and bottom.
03

Final Result

After cancelling the common terms, the simplified expression becomes \(-3\). This is the simplest form of the original expression.

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!

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

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-2}{x^{2}-25}-\frac{x-2}{25-x^{2}}$$

Two skiers begin skiing along a trail at the same time. The faster skier averages 9 miles per hour and the slower skier averages 6 miles per hour. The faster skier completes the trail \(\frac{1}{4}\) hour before the slower skier. How long is the trail?

Use similar triangles to solve. A person who is 5 feet tall is standing 80 feet from the base of a tree. The tree casts an 86 -foot shadow. The person's shadow is 6 feet in length. What is the tree's height? (IMAGE CANNOT COPY)

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{x^{2}+4 x+3}{x+2}-\frac{5 x+9}{x+2}=x-2, x \neq-2$$

Use a proportion to solve each problem. According to the authors of Number Freaking, in a global village of 200 people, 9 get drunk every day. How many of the world's 6.9 billion people \((2010\) population) get drunk everyday? Round to the nearest hundredth of a billion.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.