College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 80: 101



Work Step by Step

We simplify: $(x+1)^{3/2}+x\displaystyle *\frac{3}{2}(x+1)^{1/2} =(x+1)^{1/2}((x+1)^{2/2}+\frac{3}{2}x)=(x+1)^{1/2}(x+1+\frac{3}{2}x)=(x+1)^{1/2}(\frac{5}{2}x+1)=(x+1)^{1/2}(\frac{5}{2}x+\frac{2}{2})=\frac{1}{2}(x+1)^{1/2}(5x+2)=\frac{1}{2}\sqrt{x+1}(5x+2)$
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