Question

Aflati fractiile echiunitare de forma 9-x/7+x, 5+x/9-x, x-3/13-x, 12-x/3x, unde x∈N.

Answer 1

Ca fractiile sa fie echiunitare valoarea lor trebuie sa fie egala cu 1, deci
pt. 9-x/7+x =1; 9-x = 1·(7+x); -x-x = 7-9; -2x = -2; x=-2/-2; x=1, x∈N
pt. 5+x/9-x =1;5+x = 9-x; x + x = 9- 5;  2x = 4;  x = 4/2;  x=2, x∈N
pt. x-3/13-x=1; x-3 =13-x;  x+x=13+3; 2x=16;  x=16/2;  x=8, x∈N
pt. 12-x/3x=1; 12-x=3x;  -x-3x=-12;  -4x= -12; x=-12/-4; x=3, x∈N