Homework Help is Here – Start Your Trial Now!
Math
Algebra
**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)
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,...
See similar textbooks
icon
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.
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.

.

\frac{w+8}{w^2-11w+28}=\frac{5}{w-7}+\frac{2}{w-4}

\frac{w+8}{w^2-7w-7w+28}=\frac{5}{w-7}+\frac{2}{w-4}

\frac{w+8}{w\left(w-4\right)-7\left(w-4\right)}=\frac{5}{w-7}+\frac{2}{w-4}

\frac{w+8}{\left(w-4\right)\left(w-7\right)}=\frac{5}{w-7}+\frac{2}{w-4}

here undefined points are w=7 and w=4

multiply both sides by (w-4)(w-7)

w+8=5\left(w-4\right)+2\left(w-7\right)

w+8=5w-20+2w-14

w+8=7w-34

w+8-7w+34=0

-6w+42=0

-6w=-42

w= \frac{-42}{-6}

w= 7

but here w=7 is the undefined point

so the expression has no solution 

{\color{Red} \mathrm{No\:Solution}}

steps

Step by step

Solved in 3 steps with 40 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS