Completely factor the following: 1/2(3x-7)^(-1/2)(2x+5)^(2/3)(3)+2/3(3x-7)^(-1/2)(2x+5)^(-1/3)(2)

enmobladatn

enmobladatn

Answered question

2022-07-28

Completely factor the following:
1 2 ( 3 x 7 ) 1 2 ( 2 x + 5 ) 2 3 ( 3 ) + 2 3 ( 3 x 7 ) 1 2 ( 2 x + 5 ) 1 3 ( 2 )

Answer & Explanation

penangrl

penangrl

Beginner2022-07-29Added 17 answers

1 2 ( 3 x 7 ) 1 2 ( 2 x + 5 ) 2 3 ( 3 ) + 2 3 ( 3 x 7 ) 1 2 ( 2 x + 5 ) 1 3 ( 2 )
= ( 3 x 7 ) 1 2 ( 2 x + 5 ) 1 3 ( 3 2 ( 2 x + 5 ) 2 + 4 3 )
PoentWeptgj

PoentWeptgj

Beginner2022-07-30Added 6 answers

( 1 / 2 ) ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 2 / 3 ( 3 ) + ( 2 / 3 ) ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 ( 2 )
= ( 1 / 2 ) ( 3 ) ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 1 / 3 + ( 2 / 3 ) ( 2 ) ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 [As 1 - 1/3 = 2/3]
= ( 3 / 2 ) ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 ( 2 x + 5 ) 1 / 3 + ( 4 / 3 ) ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 [As A a b = A a A b ]
= ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 [ ( 3 / 2 ) ( 2 x + 5 ) 1 + 4 / 3 ] [taking ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 as the common factor]
= ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 [ ( 3 / 2 ) ( 2 x + 5 ) + 4 / 3 ]
= ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 [ 3 x + 15 / 2 + 4 / 3 ]
= ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 [ 3 x + 53 / 6 ] ....................[As 15/2+ 4/3 = 53/8]
Answer : ( 3 x 7 ) 1 / 2 ( 2 x + 5 ) 1 / 3 [ 3 x + 53 / 6 ]

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