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rac(45) - 7 rac(5) + rac(20)

= rac(9*5) - 7 rac(5) + rac(4*5)

= rac(9)*rac(5) - 7 rac(5) + rac(4)*rac(5)

= 3 rac(5) - 7 rac(5) + 2 rac(5)

= - 2 rac(5)

rac(75) + 3 rac(12) - 4 rac(3)

= rac( 3*25) + 3 rac(3*4) - 4 rac(3)

= rac(3)*rac(25) + 3 rac(3) rac(4) - 4 rac(3)

= 5 rac(3) + 6 rac(3) - 4 rac(3)

= 7 rac(3)

(1 - 1/3) (2/5 + 1 -1/2)
=(3/3 - 1/3) ( 4/10 + 10/10 - 5/10)

= 2/3 * 9/10
= 18/30 = 3/5


(3/4 -5/6) : (1/2 - 1/6)
= (9/12 - 10/12): ( 3/6 - 1/6)
= - 1/12 : 2/6
= -1/12 : 1/3
= - 1/12 * 3
= -3/12
= - 1/4

(3 - 2/5 + 4/3) : ( 2+4/5-2/3)
= (45/15 - 6/15 + 20/15) : ( 30/15 + 12/15 - 10/15)
= 59/15 : 32/15
=  (59/15) / (32/15)

(2/5 - 1/15)² : 4/9
=(6/15 - 1/15)² : 4/9
= (5/15)² : 4/9
= (1/3)² : 4/
= 1/9 :4/9
= 1/9 * 9/4
= 9/36
= 1/4

(3/4 - 1/2)² + (3/8 - 1/4)²
= (3/4 - 2/4)² + (3/8 - 2/8)²
= (1/4)² + (1/8)²
= 1/16 + 1/64
= 4/64 + 1/64
= 5/64

(3/4 - 1/2 * 8/3) * (2/7)²

= (3/4 - 8/6) * (2/7)²
= (9/12 - 16/12) * (2/7)²
= -7/12 * 4/49
= -28/588
= - 1 /21