Maths problem?

Comments

• hii

  June 2021

  xyz = 1

  　　x/(xy + x + 1) + y/(yz + y + 1) + z/(zx + z + 1)

  = x/(xy + x + xyz) + y/(yz + y + 1) + z/[(1/y) + z + 1)]

  = 1/(y + 1 + yz) + y/(yz + y + 1) + yz/(1 + yz + y)

  = (1 + y + yz)/(1 + y + yz) = 1
• michael-king_60bb2b61147bf

  June 2021

  x / (xy + x + 1) + y / (yz + y + 1) + z / (xz + z + 1) = 1

  [x(yz + y + 1)(xz + z + 1) + y(xy + x + 1)(xz + z + 1) + z(xy + x + 1)(yz + y + 1)] / [(xy + x + 1)(yz + y + 1)(xz + z + 1)]

  (numerator only) >> [x^2 y z^2+x^2 y z+x^2 z+x y z^2+2 x y z+x y+x z+x] + [x^2 y^2 z+x^2 y z+x y^2 z+x y^2+2 x y z+x y+y z+y] + [x y^2 z^2+x y^2 z+x y z^2+2 x y z+x z+y z^2+y z+z]

  = x^2 y^2 z+x^2 y z^2+2 x^2 y z+x^2 z+x y^2 z^2+2 x y^2 z+x y^2+2 x y z^2+6 x y z+2 x y+2 x z+x+y z^2+2 y z+y+z <<< numerator only

  (denominator only) --- x^2 y^2 z^2+x^2 y^2 z+x^2 y z^2+2 x^2 y z+x^2 z+x y^2 z^2+2 x y^2 z+x y^2+2 x y z^2+4 x y z+2 x y+2 x z+x+y z^2+2 y z+y+z+1

  ----- given that xyz = 1 sub

  denominator becomes --- x^2 y^2 z^2+x^2 y^2 z+x^2 y z^2+2 x^2 y z+x^2 z+x y^2 z^2+2 x y^2 z+x y^2+2 x y z^2+4 x y z+2 x y+2 x z+x+y z^2+2 y z+y+z+xyz

  ... compare Num. and Denom. ... are they exactly the same? then any fraction with Num. and Denom. are the same = 1