Question

Stiind a x/y =0,(6)/0,3, sa se afle rapoatele :
a) 2x-y/x-2y
b) x²+y²/2xy-y²
c)4x+7y/3y
d)8xy-x²/xy+y²

Answer 1

0,(6)=6/9=2/3
0,3=3/10
x/y=(2/3)  / (3/10)=20/9


a) (2x-y)/(x-2y)=(2x/y-1)/(x/y-2)=((2×20/9-1)/(20/9-2)=[(40-9)/9]/[(20-18)/9]=
=31/2=15,5

b) x²+y²/2xy-y² = (481/81) / (31/9) =(481/81) × (9/31) =481/2511
x²+y²=x²/y²+1=(x/y)²+1=(20/9)²+1=400/81+1=481/81
2xy-y²=2x/y-1=2×20/9-1=40/9-1=31/9

c)(4x+7y)/3y =4x/y+7 =4×20/9+7=80/9+7=(80+63)/9=143/9=15,(8)

d)(8xy-x²)/(xy+y² )=[8x/y-(x/y)²]/(x/y+1)=[8×20/9-(20/9)²]/(20/9+1)=
=(160/9-400/81) /(29/9) =1040/81 ×9/29=1040/261