Explanation Given: 2 x ( 1 − x 2 ) 1 3 + 2 3 x 3 ( 1 − x 2 ) − 2 3 ( 1 − x 2 ) 2 3 x ≠ − 1 , x ≠ 1 Formula used: Exponent rules: a − b = 1 a b ; ( − a ) m n = ( − 1 ) m n ( a ) m n . Fraction rule: b c a = b c ⋅ a . Calculation: Applying the exponent rule for the given expression 2 x ( 1 − x 2 ) 1 3 + 2 3 x 3 ( 1 − x 2 ) − 2 3 ( 1 − x 2 ) 2 3 , we get = 2 x ( 1 − x 2 ) 1 3 + 2 x 3 3 ( 1 − x 2 ) 2 3 ( 1 − x 2 ) 2 3 = 2 x ( 1 − x 2 ) 1 3 ⋅ 3 ( 1 − x 2 ) 2 3 + 2 x 3 3 ( 1 − x 2 ) 2 3 ( 1 − x 2 ) 2 3 = 2 x ( ...

10th Edition

ISBN: 9780321979476

Author: Michael Sullivan

Publisher: PEARSON

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Chapter R.8, Problem 100AE

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To find: $\frac{2 x {(1 - x^{2})}^{\frac{1}{3}} + \frac{2}{3} x^{3} {(1 - x^{2})}^{- \frac{2}{3}}}{{(1 - x^{2})}^{\frac{2}{3}}}$ $x \neq - 1, x \neq 1$

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Chapter R.8, Problem 99AE

Chapter R.8, Problem 101AE

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2 x ( 1 − x 2 ) 1 3 + 2 3 x 3 ( 1 − x 2 ) − 2 3 ( 1 − x 2 ) 2 3 x ≠ − 1 , x ≠ 1

Solution Summary: The author explains the exponent rule for the given expression: 1 x 2.

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To find: 2x ( 1 − x 2 ) 1 3 + 2 3 x 3 ( 1 − x 2 ) − 2 3 ( 1 − x 2 ) 2 3 x ≠ −1, x ≠ 1

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Chapter R Solutions

To find: $\frac{2 x {(1 - x^{2})}^{\frac{1}{3}} + \frac{2}{3} x^{3} {(1 - x^{2})}^{- \frac{2}{3}}}{{(1 - x^{2})}^{\frac{2}{3}}}$ $x \neq - 1, x \neq 1$