Solve the equation. − 5 x + 4 − 3 = x − 1 x + 4 \frac{-5}{x+4}-3=\frac{x-1}{x+4}

Hey, everyone. Let's take a look at this practice problem. So here I have negative 5 over x+4 minuteus3 is equal to x minus 1 over x plus 4, and we wanna solve this rational equation. So let's go ahead and get started with step 1, which is to determine our restriction by setting our denominator equal to 0. Now I have 2 denominators here. I have x+4 and x+4. So that means that I can just take that x+4 and set it equal to 0 to determine what my So this So this tells me that if x was equal to negative 4, that would make my denominators 0, which is what I don't want. So I know that my restriction is x cannot be equal to negative 4. Okay. So we've completed step 1. We know what x can't be. Let's go ahead and start with step 2, which is to multiply by our least common denominator. Now, again, both of my denominators here are x+4, so that means they share the common factor of x plus 4. That means that my least common denominator is simply x+4. So moving this down here to expand it, I can go ahead and write x plus 4 times my first term, negative 5 over x+4. Then my least common denominator again, and my second term, which is negative 3. And then that's equal to my least common denominator again times my last term, x minus 1 over x+4. Okay. It looks a little bit crazy right now. Let's go ahead and cancel some stuff out. So my very first term, my x+4 is going to cancel leaving me with just a negative 5. Then I'm gonna go ahead and move this 3 over to the front of those parentheses just to make it easier for me. Negative three times x+4, and that is equal to on my right side, I have x+4 canceling out again, leaving me with x minus 1. So step 2 is done and I am just left with a linear equation. Let's go ahead and do step 3, solving our linear equation. So I need to go ahead and distribute this negative 3 into those parentheses. So I have negative 5, and then negative 3 times x gives me negative 3x, and then negative 3 times 4 is going to give me negative 12. Make sure you don't lose that negative. And that's equal to my right side x minus 1. Now I do have some like terms that need to get combined here. I have this negative 5 and this negative 12, which is going to combine to give me negative 17. Then pulling my 3 x down, I have 7 negative 17 minus 3 x is equal to x minus 1. Nothing needs to get combined over there. And now we can move all of our x terms to one side, all of our constants to the other. So I wanna go ahead and move this x over here, move my 17 over here. So in order to do that, I can subtract x, letting it cancel, and then add 17 to both sides. It will, of course, cancel there. I'm left with negative 3x minus x, which will give me negative 4x, and that's equal to negative 1 +17, which will give me 16. Now my very last step is to isolate x. And to do that, I need to divide both sides by negative 4. So my negative 4 will cancel there, and I'm left with x is equal to 16 divided by negative 4 which is negative 4 and here is my solution. So step 3 is done but we cannot forget step 4 which is to check our solution with our restriction. Now my restriction was that x could not be equal to negative 4, and my solution that I got was that x equals negative 4. So this tells me that this is not my solution, and I actually have no solution because my answer was equal to my restriction which we know is what it can't be. So that's all for this one, I'll see you in the next one.

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1. Review of Real Numbers2h 39m

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
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

Formulas
21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 17m

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

5. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

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
33m

Quadratic Equations & Applications
41m

8. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

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

9. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

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38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

10. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

11. 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

12. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

13. Inverse, Exponential, & Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

14. Conic Sections & Systems of Nonlinear Equations2h 24m

Graphing Circles
32m

Ellipses
35m

Parabolas
35m

Hyperbolas
41m

15. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

8. Rational Expressions and Equations

Rational Equations

Beginning & Intermediate Algebra

8. Rational Expressions and Equations

Rational Equations

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Solve the equation.
$\frac{- 5}{x + 4} - 3 = \frac{x - 1}{x + 4}$

$x=4$

$x=1$

$x = - 1$

No solution

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Problema precedenteProssimo problema

Guida verificata passo dopo passo

Identify the given equation: $\frac{-5}{x+4} - 3 = \frac{x-1}{x+4}$.

Notice that the denominators on both fractions are the same, $x+4$, so we should consider the domain restriction: $x \neq -4$ to avoid division by zero.

To eliminate the fractions, multiply every term in the equation by the common denominator $(x+4)$ to clear the denominators.

After multiplying, simplify the resulting equation by distributing and combining like terms carefully.

Solve the simplified equation for $x$ and then check if the solutions satisfy the original equation and the domain restriction; if none do, conclude that there is no solution.