Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set - Page 524: 37


This equation has no solution.

Work Step by Step

$\dfrac{y}{2y+2}+\dfrac{2y-16}{4y+4}=\dfrac{2y-3}{y+1}$ Take out common factor $2$ from the denominator of the first fraction and common factor $4$ from the denominator of the second fraction: $\dfrac{y}{2(y+1)}+\dfrac{2y-16}{4(y+1)}=\dfrac{2y-3}{y+1}$ Multiply the whole equation by $8(y+1)$ $8(y+1)\Big[\dfrac{y}{2(y+1)}+\dfrac{2y-16}{4(y+1)}=\dfrac{2y-3}{y+1}\Big]$ $4y+4y-32=16y-24$ Take all terms to the right side of the equation and simplify it by combining like terms: $16y-24-4y-4y+32=0$ $8y+8=0$ Solve for $y$: $8y=-8$ $y=-\dfrac{8}{8}$ $y=-1$ This is the solution found. Substituting $y=-1$ in the original equation makes all denominator $0$. Knowing that, we conclude that this equation has no solution.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.