Question

Stiind ca 2x supra 9y =0,291,(6) , calculati 8x-3y supra 4x+5y

Answer 1

2x/9y=0,291(6)
2x/9y=(2916-291)/9000
2x/9y=2625/9000
2x/9y=105/360
2x/9y=21/72
2x/9y=7/24
y=16x/21

(8x-3y)/(4x+5y)=
=(8x-3×16x/21)/(4x+5×16x/21)=
=(8x-16x/7)/(4x+80x/21)=
=[(56x-16x)/7]/[(84x+80x)/21]=
=(40x/7)/(164x/21)=
=(40x/7)  × (21/164x)=
=(10/1)  × (3/41)=
=30/41