Question

[(1/3)² +(4/5)² -(7/15)²] : [(37/30)² - (7/6)²] :3,(3)= ?

Answer 1

[ ( 1/3)^2 + ( 4/5)^2 - ( 7/3 x 5)^2 ]  : [ ( 37/ 5^2 x 6^2 - 7/6^2 ] : 10/3 =
= [ ( 5^2 + 4 x 3 ^2 - 7^2)/3^2 x 5^2 ] : [ (37^2 - 7^2 x 5^2 ) / 5^2 x 6^2 ] : 10/3 =
= [ ( 25 + 4 x 9 - 49 )/ 3^2x5^2 ] : [ (37^2 - 35^2) / 5^2 x 6^2 ] : 10/3 =
= (12 / 3^2 x 5^2 ) : ( 1369 - 1225 ) / 5^2 x 6^2 ) x 3/10 =
= (12/ 3^2 x 5^2 ) : ( 144/ 5^2 x 6^2 ) x 3/10 =
= ( 12/ 3^2 x 5^2 ) x (5^2 x 6^2)/144 x 3/10 = 
= ( 12 x 5^2 x 6^2 x 3 ) / 3^2 x 5^2 x 144 x 10 =
= ( 12 x 5^2 x 2^2 x 3^2 x 3 ) / 3^2 x 5^2 x 12^2 x 10 =
= ( 12 x 2^2 x 3^2 x 3 ) / 3^2 x 12^2 x 10 =
= ( 2^2 x 3^2 x 3 ) / 3^2 x 12 x 10 =
= ( 2^2 x 3 ) / 12 x 10 =
= 12 / 12 x 10 =
= 1/10