(9-√3)/(√3) + 6/(√5+3) simplify
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see your answer in pic.
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Nee621:
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Hi ,
1 ) ( 9 - √3 ) / √3
= [ √3 ( 9 - √3 ) ]/( √3 × √3 )
= ( 9√3 - 3 )/3 ---( 1 )
2 ) 6/( √5 + 3 )
= [ 6( 3 - √5 ) ]/[ ( 3 + √5 )( 3- √5 )]
= [ 6( 3 - √5 ) ] /[ 3² - ( √5 )² ]
= [ 6( 3 - √5 ) ]/( 9 - 5 )
= [ 6( 3 - √5 )]/4
= 3( 3 - √5 )/2
= ( 9 - 3√5 )/2 ---( 2 )
Now ,
( 9 - √3 )/√3 + 6/( √5 + 3 )
= ( 1 ) + ( 2 )
= ( 9√3 - 3 )/3 + ( 9 - 3√5 )/2
= [ 2(9√3 - 3 ) + 3( 9 - 3√5 )]/6
= ( 18√3 - 6 + 27 - 9√5 )/6
= ( 21 + 18√3 - 9√5 )/6
= [ 3 ( 7 + 6√3 - 3√5 ) ]/6
= ( 7 + 6√3 - 3√5 )/2
I hope this helps you.
: )
1 ) ( 9 - √3 ) / √3
= [ √3 ( 9 - √3 ) ]/( √3 × √3 )
= ( 9√3 - 3 )/3 ---( 1 )
2 ) 6/( √5 + 3 )
= [ 6( 3 - √5 ) ]/[ ( 3 + √5 )( 3- √5 )]
= [ 6( 3 - √5 ) ] /[ 3² - ( √5 )² ]
= [ 6( 3 - √5 ) ]/( 9 - 5 )
= [ 6( 3 - √5 )]/4
= 3( 3 - √5 )/2
= ( 9 - 3√5 )/2 ---( 2 )
Now ,
( 9 - √3 )/√3 + 6/( √5 + 3 )
= ( 1 ) + ( 2 )
= ( 9√3 - 3 )/3 + ( 9 - 3√5 )/2
= [ 2(9√3 - 3 ) + 3( 9 - 3√5 )]/6
= ( 18√3 - 6 + 27 - 9√5 )/6
= ( 21 + 18√3 - 9√5 )/6
= [ 3 ( 7 + 6√3 - 3√5 ) ]/6
= ( 7 + 6√3 - 3√5 )/2
I hope this helps you.
: )
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