Question

Va rog frumos,imi trebuie urgent.Aduceti la o forma mai simpla:
a)ax+ay-bx-by supta xy+x^2
b)x^2-2x+1 supra y-xy+z-zx
c)y^2+x^2-2xy supra xz-yz+ty-xt
d)xy-xz-y^2+yz supra x^2-xy
va rog frumos pe lung.

Answer 1

a) (ax+ay-bx-by )/( xy+x²) =
= [a(x+y)-b(x+y)]/x( y+x) =
= (x+y)(a-b)/x( y+x) =
= (a-b)/x

b)(x²-2x+1)/(y-xy+z-zx)=
=(x-1)²/[y(1-x)+z(1-x)]=
=(x-1)²/[-(x-1)(y+z)]=
=(x-1)/[-(y+z)]=
=(1-x)/(y+z)

c)y²+x²-2xy/(xz-yz+ty-xt)=
=(x-y)²/[z(x-y)-t(x-y)=
=(x-y)²/(x-y)(z-t)=
=(x-y)/(z-t)

d)(xy-xz-y²+yz) /( x²-xy)=
=[x(y-z)-y(y-z)] /x( x-y)=
=(y-z)(x-y) /x( x-y)=
=(y-z) /x