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: 37

Answer

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.
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