un exo facile

salam

on a x et y des nombre ........

demontez que

(x^-1+y^-1)^-1= (xy)/(x+y)


et demontrer que

(x+y)^-1*(x^-1+y^-1)=x^-1 *y^-1



@@@@@++++++

salut
pour 1)
(x^-1+y^-1)^-1
=(1/x+1/y)^-1
=(x+y/xy)^-1
=xy/x+y

salut!!
pour 2)(x+y)^-1*(x^-1+y^-1)=x^-1 *y^-1
(x+y)^-1*(x^-1+y^-1)
=1/x+y * 1/x + 1/y
= 1/x(x+y) + 1/y(x+y)
=1/(x²+xy) + 1/(yx+y²)
nowa77id lma9am
=(x²+xy+xy+y²) / (x²+xy)(yx+y²)
=(x²+2xy+y²) / (yx^3+x²y²+y²x²+xy^3)
=(x+y)² / yx(x²+2xy+y²)
=(x+y)² / xy(x+y)²
=1/xy
= 1/x * 1/y
=x^-1 * y^-1
@++++++++++

juste!

c vrais