Subtract the following and simplify the difference if possible. x 2 − 4 x 2 − x − 6 − x + 2 x 2 − x − 6 \frac{x^2-4}{x^2-x-6}-\frac{x+2}{x^2-x-6}

This problem asks us to subtract the following and simplify the difference if possible. So we have x squared minus four over x squared minus x minus six, and then we have all of that minus x plus two over x squared minus x minus six. Now what I first need to do is look at my two rational expressions that are being subtracted, and see if we have a common denominator. Since I can see that we clearly do, that means I just need to combine the numerators and keep the common denominator. So we'll have x squared minus four, minus x plus two, and all of this is going to be over the common denominator of x squared minus x minus six. Now from here, I can simplify the numerator. Subtracting these quantities is the same thing as having a negative one in front of this first or in front of the second quantity and then adding. It. So in this case, we can keep the x squared minus four the same, then I can just distribute the negative sign into each of these terms. So that'll give me negative x and then negative two, and then we'll this will all be over x squared minus x minus six. So So this is what we get. Now from here I can combine like terms on top. Notice we have a negative four and a negative two, that will combine to give us negative six. So we end up with x squared minus x minus six, and that's all going to be over x squared minus x minus six. And notice something here. We have the same quadratic on top that we do on bottom, the same numerator and the same denominator. We could factor each of these, but we don't actually have to since we can see they're the same thing. So we just know that all of this is going to cancel and reduce down to just giving us one. So one would be the solution to this problem, and that's how you can solve it.

Subtract the following and simplify the difference if possible.x2−4x2−x−6−x+2x2−x−6\frac{$$x^2-4$$}{$$x^2-x-6$$}-\frac{x+2}{$$x^2-x-6$$}

x−3x+2\frac{x-3}{x+2}x+2x−3

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1. Review of Real Numbers2h 43m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

3. Solving Word Problems2h 46m

Introduction to Problem Solving
37m

Formulas
25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
15m

Composition of Functions
17m

5. Systems of Linear Equations1h 53m

Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

6. Exponents, Polynomials, and Polynomial Functions3h 17m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
38m

Special Products
34m

7. Factoring2h 49m

Factoring by Greatest Common Factor & Grouping
38m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
41m

Quadratic Equations & Applications
41m

8. Rational Expressions and Functions3h 44m

Simplifying Rational Expressions
42m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

9. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

10. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

11. Inverse, Exponential, & Logarithmic Functions2h 30m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
54m

12. Conic Sections & Systems of Nonlinear Equations2h 24m

Graphing Circles
32m

Ellipses
35m

Parabolas
35m

Hyperbolas
41m

13. Sequences, Series, and the Binomial Theorem1h 50m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
29m

Factorials
13m

8. Rational Expressions and Functions

Adding and Subtracting Rational Expressions with Common Denominators

Intermediate Algebra

8. Rational Expressions and Functions

Adding and Subtracting Rational Expressions with Common Denominators

Problema precedenteProssimo problema

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Scelta multipla

Subtract the following and simplify the difference if possible.
$\frac{x^{2} - 4}{x^{2} - x - 6} - \frac{x + 2}{x^{2} - x - 6}$

$\frac{1}{x - 3}$

$x$

$1$

$\frac{x-3}{x+2}$

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Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify that both fractions have the same denominator $x^2 - x - 6$, so you can combine the numerators directly by subtraction over the common denominator.

Write the expression as a single fraction: $\frac{x^2 - 4 - (x + 2)}{x^2 - x - 6}$.

Simplify the numerator by distributing the negative sign and combining like terms: $x^2 - 4 - x - 2$.

Factor the numerator and denominator if possible. Recall that $x^2 - 4$ factors as $(x - 2)(x + 2)$ and $x^2 - x - 6$ factors as $(x - 3)(x + 2)$.

Cancel any common factors between numerator and denominator to simplify the fraction to its lowest terms.

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Difficoltà con Intermediate Algebra?

Subtract the following and simplify the difference if possible.x2−4x2−x−6−x+2x2−x−6\(\frac{x^2-4}{x^2-x-6}\)-\(\frac{x+2}{x^2-x-6}\)

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Set di pratica su Adding and Subtracting Rational Expressions with Common Denominators

Subtract the following and simplify the difference if possible.
$\frac{x^{2} - 4}{x^{2} - x - 6} - \frac{x + 2}{x^{2} - x - 6}$