Question

verificati relatiile
$\frac{a + b}{a \times b}$
egal cu
$\frac{1}{a} + \frac{1}{b}$
si
$\frac{a - b}{a \times b}$
egal cu
$\frac{1}{b} - \frac{1}{a}$
va rog mult de tot

Answer 1

(a+b)/(a×b) = 1/a + 1/b
__________________
Fie 1/a + 1/b
se aduce la acelasi numitor
b/(a×b) + a/(b×a) = (a+b)/(a×b)



(a-b)/(a×b)=1/a - 1/b
__________________
Fie 1/a - 1/b
se aduce la acelasi numitor
b/(a×b) - a/(b×a) = (a-b)/(a×b)

Answer 2

1 / a + 1 / b =  b / ( a x b ) + a / ( a x b ) = ( b + a )/ ( a x b)= ( a + b ) / (a x b )

→ b + a = a + b ⇔  adunarea este comutativa

1 / a - 1 / b = b / ( a x b ) - a / ( a x b ) = ( b - a ) / ( a x b ) → c.c.t.d.