**Title: Solving Rational Equations** **Section: Problems** **Instruction: Solve each rational equation.** 10. \[ \frac{w+8}{w^2 - 11w + 28} = \frac{5}{w-7} + \frac{2}{w-4} \] 11. \[ \frac{x}{x+7} - 8 = \frac{98}{x^2 - 49} \] 12. \[ \frac{5}{x^2 + 4x + 3} + \frac{2}{x^2 + x - 6} = \frac{3}{x^2 - x - 2} \] **Instructions for the Student:** - Simplify each equation and solve for the variable. - Identify any restrictions on the variable based on the denominators. - Consider factoring to simplify and solve the equations, especially for quadratic expressions in the denominator. **Note:** Check your solutions by plugging them back into the original equations to ensure they do not make any denominators zero.
**Title: Solving Rational Equations** **Section: Problems** **Instruction: Solve each rational equation.** 10. \[ \frac{w+8}{w^2 - 11w + 28} = \frac{5}{w-7} + \frac{2}{w-4} \] 11. \[ \frac{x}{x+7} - 8 = \frac{98}{x^2 - 49} \] 12. \[ \frac{5}{x^2 + 4x + 3} + \frac{2}{x^2 + x - 6} = \frac{3}{x^2 - x - 2} \] **Instructions for the Student:** - Simplify each equation and solve for the variable. - Identify any restrictions on the variable based on the denominators. - Consider factoring to simplify and solve the equations, especially for quadratic expressions in the denominator. **Note:** Check your solutions by plugging them back into the original equations to ensure they do not make any denominators zero.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Title: Solving Rational Equations**
**Section: Problems**
**Instruction: Solve each rational equation.**
10. \[
\frac{w+8}{w^2 - 11w + 28} = \frac{5}{w-7} + \frac{2}{w-4}
\]
11. \[
\frac{x}{x+7} - 8 = \frac{98}{x^2 - 49}
\]
12. \[
\frac{5}{x^2 + 4x + 3} + \frac{2}{x^2 + x - 6} = \frac{3}{x^2 - x - 2}
\]
**Instructions for the Student:**
- Simplify each equation and solve for the variable.
- Identify any restrictions on the variable based on the denominators.
- Consider factoring to simplify and solve the equations, especially for quadratic expressions in the denominator.
**Note:** Check your solutions by plugging them back into the original equations to ensure they do not make any denominators zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf4d7820-5684-4d56-9f10-efdcf5b1ca91%2F01c6fc59-5c71-44f4-9c69-42dc686a7110%2Fzn10sn9.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving Rational Equations**
**Section: Problems**
**Instruction: Solve each rational equation.**
10. \[
\frac{w+8}{w^2 - 11w + 28} = \frac{5}{w-7} + \frac{2}{w-4}
\]
11. \[
\frac{x}{x+7} - 8 = \frac{98}{x^2 - 49}
\]
12. \[
\frac{5}{x^2 + 4x + 3} + \frac{2}{x^2 + x - 6} = \frac{3}{x^2 - x - 2}
\]
**Instructions for the Student:**
- Simplify each equation and solve for the variable.
- Identify any restrictions on the variable based on the denominators.
- Consider factoring to simplify and solve the equations, especially for quadratic expressions in the denominator.
**Note:** Check your solutions by plugging them back into the original equations to ensure they do not make any denominators zero.
Expert Solution

Question-10
Since you have asked multiple questions, we will solve the first(all 3 parts) question for you.
If you want any specific question to be solved then please specify the question number or post only that question.
.
NOTE: Refresh your page if you can't see any equations.
.
here undefined points are w=7 and w=4
multiply both sides by (w-4)(w-7)
but here w=7 is the undefined point
so the expression has no solution
Step by step
Solved in 3 steps with 40 images

Recommended textbooks for you

Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON

Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning

Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning

Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON

Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning

Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning

Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON

Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press

College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education