$A=\frac{-2}{9}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{15}+\frac{1}{57}+\frac{1}{3}-\frac{1}{36}$

$\to A=(\frac{-2}{9}+\frac{-3}{4}+\frac{1}{3}-\frac{1}{36})+(\frac{3}{5}+\frac{1}{15})+\frac{1}{57}$

$\to A=(\frac{-8}{36}+\frac{-27}{36}+\frac{12}{36}-\frac{1}{36})+(\frac{9}{15}+\frac{1}{15})+\frac{1}{57}$

$\to A=\frac{-2}{3}+\frac{2}{3}+\frac{1}{57}$

$\to A=0+\frac{1}{57}$

$\to A=\frac{1}{57}$

Vậy $A=\frac{1}{57}$

Gọi $ƯCLN(12n+1,30n+2)=d(d>0,d\in Z)$

$\Rightarrow 12n+1⋮d,30n+2⋮d$

$\Rightarrow 60n+5⋮d,60n+4⋮d$

$\Rightarrow 60n+5-60n-4⋮d$

$\Rightarrow 1⋮d$

$\Rightarrow d\in Ư\left(1\right)=\{1,-1\}$

$\Rightarrow \frac{12n+1}{30n+2}$ là phân số tối giản với mọi số nguyên n

Gọi $ƯCLN(12n+1,30n+2)=d(d>0,d\in Z)$

$\Rightarrow 12n+1⋮d,30n+2⋮d$

$\Rightarrow 60n+5⋮d,60n+4⋮d$

$\Rightarrow 60n+5-60n-4⋮d$

$\Rightarrow 1⋮d$

$\Rightarrow d\in Ư\left(1\right)=\{1,-1\}$

$\Rightarrow \frac{12n+1}{30n+2}$ là phân số tối giản với mọi số nguyên n

\(\dfrac{-2}{9}-\dfrac{3}{4}+\dfrac{3}{5}+\dfrac{1}{15}+\dfrac{1}{57}+\dfrac{1}{3}-\dfrac{1}{36}\)

\(=\left(-\dfrac{2}{9}-\dfrac{3}{4}-\dfrac{1}{36}\right)+\left(\dfrac{3}{5}+\dfrac{1}{15}+\dfrac{1}{3}\right)+\dfrac{1}{57}\)

\(=\dfrac{-8-27-1}{36}+\dfrac{9+1+5}{15}+\dfrac{1}{57}\)

\(=-\dfrac{36}{36}+\dfrac{15}{15}+\dfrac{1}{57}\)

\(=\dfrac{1}{57}\)

\(A=\frac{-2}{9}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{15}+\frac{1}{57}+\frac{1}{3}+\frac{-1}{36}\)

\(A=\left(\frac{-2}{9}+\frac{-3}{4}+\frac{1}{3}+\frac{-1}{36}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)+\frac{1}{57}\)

\(A=\left(\frac{-8}{36}+\frac{-27}{36}+\frac{12}{36}+\frac{-1}{36}\right)+\left(\frac{9}{15}+\frac{1}{15}\right)+\frac{1}{57}\)

\(A=\frac{-2}{3}+\frac{2}{3}+\frac{1}{57}\)

\(A=\frac{-38}{57}+\frac{38}{57}+\frac{1}{57}\)

\(A=\frac{1}{57}\)

A=\(\dfrac{-2}{9}\)+\(\dfrac{-3}{4}\)+\(\dfrac{3}{5}\)+\(\dfrac{1}{15}\)+\(\dfrac{1}{57}\)+\(\dfrac{1}{3}\)+\(\dfrac{-1}{36}\)

A=(\(\dfrac{-2}{9}\)+\(\dfrac{-3}{4}\)+\(\dfrac{-1}{36}\))+(\(\dfrac{3}{5}\)+\(\dfrac{1}{15}\)+\(\dfrac{1}{3}\))

A=1/57

B=1/41

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