College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 48: 64

Answer

$-\frac{3}{y+3}$

Work Step by Step

1. LCD of all the fractions is found by multiplying the two denominators $y +3$ and $y$ to get $y(y + 3)$. 2. Multiply the numerators and denominators by the LCD: $\frac{\frac{1}{y + 3} - \frac{1}{y}}{\frac{1}{y}} = \frac{\left(\frac{1}{y + 3} - \frac{1}{y}\right)\cdot y (y + 3)}{\frac{1}{y} \cdot y (y + 3)}$ 3. Distribute to multiply: $\frac{\left(\frac{1}{y + 3} - \frac{1}{y}\right)\cdot y (y + 3)}{\frac{1}{y} \cdot y (y + 3)} = \frac{\frac{y(y + 3)}{y + 3} - \frac{y (y + 3)}{y}}{\frac{1}{y} y (y+3)}$ $=\frac{y - (y + 3)}{y + 3}$ $=-\frac{3}{y+3}$
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