Simplify the expression. ((x+2)^(3/4)(x+3)^(-2/3)-(x+3)^(1/3)(x+2)^(1/4))/[(x+2)^(3/4)]^2 (2(3x-1)^(1/3)-(2x+1)(1/3)(3x)(3x-1)^(-2/3)3)/((3x-1)^(2/3))

Matilda Fox

Matilda Fox

Answered question

2022-07-26

Simplify the expression.
( ( x + 2 ) 3 / 4 ( x + 3 ) 2 / 3 ( x + 3 ) 1 / 3 ( x + 2 ) 1 / 4 ) / [ ( x + 2 ) 3 / 4 ] 2
2 ( 3 x 1 ) 1 / 3 ( 2 x + 1 ) ( 1 / 3 ) ( 3 x 1 ) 2 / 3 3 ( 3 x 1 ) 2 / 3

Answer & Explanation

sweetwisdomgw

sweetwisdomgw

Beginner2022-07-27Added 20 answers

1. ( ( x + 2 ) 3 / 4 ( x + 3 ) 2 / 3 ( x + 3 ) 1 / 3 ( x + 2 ) 1 / 4 ) / [ ( x + 2 ) 3 / 4 ] 2
( x + 3 ) 2 / 3 ( x + 2 ) 1 / 4 [ ( x + 2 ) ( x + 3 ) ] ( x + 2 ) 3 / 2 = 1 ( x + 3 ) 2 / 3 ( x + 2 ) 1 / 4 ( x + 2 ) 3 / 2
= 1 ( x + 3 ) 2 / 3 ( x + 2 ) 7 / 4
2. 2 ( 3 x 1 ) 1 / 3 ( 2 x + 1 ) ( 1 / 3 ) ( 3 x 1 ) 2 / 3 3 ( 3 x 1 ) 2 / 3
= ( 3 x 1 ) 2 / 3 [ 2 ( 3 x 1 ) ( 2 x + 1 ) ] ( 3 x 1 ) 2 / 3
= 6 x 2 2 x 1 ( 3 x 1 ) 4 / 3 = 4 x 3 ( 3 x 1 ) 4 / 3

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