/*! 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 40 Add or subtract as indicated. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 40

Add or subtract as indicated. $$\frac{x^{2}-4 x}{x^{2}-x-6}-\frac{x-6}{x^{2}-x-6}$$

Short Answer

Expert verified
The result of the subtraction is \( \frac{x-3}{x+3} \).

Step by step solution

01

Identifying like terms

In the given exercise, the denominators of both fractions are the same: \(x^{2}-x-6\). The numerators are \(x^{2}-4x\) and \(x-6\). The aim is to subtract the second fraction from the first.
02

Subtracting fractions

Since the denominators are the same, the fractions can be subtracted by subtracting the numerators. This gives: \(\frac{x^{2}-4x-(x-6)}{x^{2}-x-6}\).
03

Simplifying the Fraction

Distribute the negative sign in the numerator: \(\frac{x^{2}-4x-x+6}{x^{2}-x-6}\), and combine like terms to give: \(\frac{x^{2}-5x+6}{x^{2}-x-6}\).
04

Factoring the numerator and denominator

Factoring the numerator and denominator results in: \(\frac{(x-2)(x-3)}{(x-2)(x+3)}\).
05

Simplifying the Fraction

The term (x-2) is in both the numerator and the denominator, so it cancels out, leaving the simplified fraction as: \( \frac{x-3}{x+3}\).

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

Simplify by reducing the index of the radical. $$\sqrt[4]{x^{12}}$$

Evaluate each expression. $$\sqrt[3]{\sqrt{\sqrt{169}+\sqrt{9}}+\sqrt{\sqrt[3]{1000}+\sqrt[3]{216}}}$$

Simplify each expression. Assume that all variables represent positive numbers. $$ \left(\frac{x^{-\frac{5}{4} y^{\frac{1}{3}}}}{x^{-\frac{3}{4}}}\right)^{-6} $$

Place the correct symbol, \(>\) or \(<,\) in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. $$\text { a. } 3^{\frac{1}{2}} \square 3^{\frac{1}{3}}$$ $$\text { b. } \sqrt{7}+\sqrt{18} \square \sqrt{7}+18$$

In Exercises 132鈥�135, determine whether each statement makes sense or does not make sense, and explain your reasoning. There are many exponential expressions that are equal to \(36 x^{12},\) such as \(\left(6 x^{6}\right)^{2},\left(6 x^{3}\right)\left(6 x^{9}\right), 36\left(x^{3}\right)^{9},\) and \(6^{2}\left(x^{2}\right)^{6}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

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.