RΔspuns :
a)
β288/27+β1 24/48 +β3 27/72 -β1250/108 =
=β288/27+β72/48 +β243/72 -β1250/108 =
=β32/3+β3/2 +β27/8 -β625/54 =
=4β2/β3+β3/β2 +β27/2β2 -25/3β6 =
=4β6/3+β6/2 +3β6/4 -25β6/18 =
=(48β6+18β6 +27β6 -50β6)/36 =
=43β6/36
b)
β32/81-β(12+2/4)+β(2+26/36) -β(1+2/16) =
=β32/81-β50/4+β98/36 -β18/16 =
=β32/β81-β50/β4+β98/β36 -β18/β16 =
=4β2/9-5β2/2+7β2/6 -3β2/4 =
=(16β2-90β2+42β2 -27β2)/36 =
=(16β2-90β2+42β2 -27β2)/36 =
=-59β2/36
c)
β18 3/8-β(42+2/3)+β(13 1/2) -(β4 1/6- β10 2/3) =
=β147/8-β128/3+β27/2 -β25/6+ β32/3 =
=7β3/2β2-8β2/β3+3β3/β2 -5/β6+ 4β2/β3 =
=7β6/4-8β6/3+3β6/2 -5β6/6+ 4β6/3 =
=(21β6-32β6+18β6 -10β6+ 16β6)/12 =
=13β6/12
d) (4-3β6)/2β3 -(5β6-7)/4β2 +(3+2β6)/5β3 -(4β6-3)/6β2=
= (4-3β6)β3/6 -(5β6-7)β2/8 +(3+2β6)β3/15 -(4β6-3)β2/12=
= (4β3-3β18)/6 -(5β12-7β2)/8 +(3β3+2β18)/15 -(4β12-3β2)/12=
= (4β3-9β2)/6 -(10β3-7β2)/8 +(3β3+6β2)/15 -(8β3-3β2)/12=
= (4β3-9β2)/6 -(10β3-7β2)/8 +(β3+2β2)/5 -(8β3-3β2)/12=
= (80β3-180β2 -150β3+105β2 +24β3+48β2 -80β3+30β2)/120=
= ( 3β2 -126β3)/120=(β2 -42β3)/40
β288/27+β1 24/48 +β3 27/72 -β1250/108 =
=β288/27+β72/48 +β243/72 -β1250/108 =
=β32/3+β3/2 +β27/8 -β625/54 =
=4β2/β3+β3/β2 +β27/2β2 -25/3β6 =
=4β6/3+β6/2 +3β6/4 -25β6/18 =
=(48β6+18β6 +27β6 -50β6)/36 =
=43β6/36
b)
β32/81-β(12+2/4)+β(2+26/36) -β(1+2/16) =
=β32/81-β50/4+β98/36 -β18/16 =
=β32/β81-β50/β4+β98/β36 -β18/β16 =
=4β2/9-5β2/2+7β2/6 -3β2/4 =
=(16β2-90β2+42β2 -27β2)/36 =
=(16β2-90β2+42β2 -27β2)/36 =
=-59β2/36
c)
β18 3/8-β(42+2/3)+β(13 1/2) -(β4 1/6- β10 2/3) =
=β147/8-β128/3+β27/2 -β25/6+ β32/3 =
=7β3/2β2-8β2/β3+3β3/β2 -5/β6+ 4β2/β3 =
=7β6/4-8β6/3+3β6/2 -5β6/6+ 4β6/3 =
=(21β6-32β6+18β6 -10β6+ 16β6)/12 =
=13β6/12
d) (4-3β6)/2β3 -(5β6-7)/4β2 +(3+2β6)/5β3 -(4β6-3)/6β2=
= (4-3β6)β3/6 -(5β6-7)β2/8 +(3+2β6)β3/15 -(4β6-3)β2/12=
= (4β3-3β18)/6 -(5β12-7β2)/8 +(3β3+2β18)/15 -(4β12-3β2)/12=
= (4β3-9β2)/6 -(10β3-7β2)/8 +(3β3+6β2)/15 -(8β3-3β2)/12=
= (4β3-9β2)/6 -(10β3-7β2)/8 +(β3+2β2)/5 -(8β3-3β2)/12=
= (80β3-180β2 -150β3+105β2 +24β3+48β2 -80β3+30β2)/120=
= ( 3β2 -126β3)/120=(β2 -42β3)/40