/*! 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 32 In Exercises \(1-46,\) solve eac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 32

In Exercises \(1-46,\) solve each rational equation. $$\frac{2}{y-2}=\frac{y}{y-2}-2$$

Short Answer

Expert verified
The equation has no solution as it leads to an undefined operation.

Step by step solution

01

Simplifying Rational Equation

Since the denominator on both sides is \(y - 2\), it can be eliminated by multiplying the entire equation by \(y - 2\). This yields: \(2 = y - 2(y - 2)\)
02

Distributing and simplifying the equation

Now distribute the equation to simplify. So it yields: \(2 = y - 2y + 4\) which simplifies to: \(2 = - y + 4\).
03

Re-arranging the equation

To find the value of \(y\), rearrange the equation to isolate \(y\) which yields : \(y = 4 - 2\).
04

Solving for y

Solving for \(y\) gives \(y = 2\). However, substituting \(y = 2\) into the original equation, we notice that the denominator becomes zero, which is undefined in terms of mathematical operations. Therefore, the original equation has no solution.

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

Perform the indicated operation or operations. Simplify the result, if possible. $$\frac{3}{x^{2}+4 x y+3 y^{2}}-\frac{5}{x^{2}-2 x y-3 y^{2}}+\frac{2}{x^{2}-9 y^{2}}$$

In Palo Alto, California, a government agency ordered computer-related companies to contribute to a pool of money to clean up underground water supplies. (The companies had stored toxic chemicals in leaking underground containers.) The formula $$ C=\frac{2 x}{100-x} $$ models the cost, \(C\), in millions of dollars, for removing \(x\) percent of the contaminants. Use this mathematical model to solve Exercises \(71-72\). What percentage of the contaminants can be removed for \(\$ 2\) million?

Multiply: \(\quad(3 x+5)(2 x-7)\).

Add or subtract as indicated. Simplify the result, if possible. $$\frac{y+3}{5 y^{2}}-\frac{y-5}{15 y}$$

Describe similarities and differences between the procedures needed to solve the following problems: $$ \text { Add: } \frac{2}{x}+\frac{3}{4}, \quad \text { Solve: } \frac{2}{x}+\frac{3}{4}=1 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.