/*! 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 76 Simplify each rational expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 76

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x^{2}+3 x y-10 y^{2}}{3 x^{2}-7 x y+2 y^{2}}$$

Short Answer

Expert verified
The simplified rational expression is \(\frac{x+5y}{3x - y}\).

Step by step solution

01

Factorizing the Numerator

Start by trying to factorize the numerator, which resembles a quadratic expression of the form \(ax^2 + bx + c\). Subsequently, this equation turns into \((x+5y)(x-2y)\) through factorization.
02

Factorizing the Denominator

Similarly, factorize the denominator, which also resembles a quadratic equation. The denominator turns into \((3x - 2y)(x - y)\) through factorization.
03

Simplify the Rational Expression

Now having both the numerator and the denominator factorized, the goal is to simplify the complex fraction. Look for the common factors between the numerator and the denominator. The common factor is \((x-2y)\) which can be cancelled out to obtain the simplified rational expression.
04

Final Simplification

After reducing common factors, we have \(\frac{x+5y}{3x - y}\) as the simplified rational 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

Add or subtract as indicated. Simplify the result, if possible. $$\frac{4}{x}+\frac{3}{x-5}$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{3 x}{(x+1)^{2}}-\left[\frac{5 x+1}{(x+1)^{2}}-\frac{3 x+2}{(x+1)^{2}}\right]$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{y}{a x+b x-a y-b y}-\frac{x}{a x+b x-a y-b y}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{11}{x+7}-\frac{5}{-x-7}$$

add or subtract as indicated. Simplify the result, if possible. $$\begin{aligned} &\frac{x^{2}+9 x}{4 x^{2}-11 x-3}+\frac{3 x-5 x^{2}}{4 x^{2}-11 x-3}\\\ &x^{2}-4 x-4 x-4 \end{aligned}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied 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.