Question

Tính :1/a - 1/b    với b = a + 1

so sánh :   1/a . b với 1/a - 1/b

Answer 1

\(\frac{1}{a}-\frac{1}{b}=\frac{1}{a}-\frac{1}{a+1}=\frac{a+1}{a\left(a+1\right)}-\frac{a}{a\left(a+1\right)}=\frac{1}{a\left(a+1\right)}\)

\(\frac{1}{a}.\frac{1}{b}=\frac{1}{a}.\frac{1}{a+1}=\frac{1}{a\left(a+1\right)}\)

vậy \(\frac{1}{a}-\frac{1}{b}=\frac{1}{a}.\frac{1}{b}\)

Answer 2

\(\frac{1}{a}-\frac{1}{b}\) với b = a + 1

= \(\frac{b}{a.b}-\frac{a}{a.b}\)

= \(\frac{b-a}{a.b}\)

= \(\frac{a+1-a}{a.b}\)

= \(\frac{1}{a.b}\)

Vậy \(\frac{1}{a.b}=\frac{1}{a}-\frac{1}{b}\)